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We discuss the discrete as well as the continuous symmetry transformations for a three $(2+1)$-dimensional $(3D)$ combined system of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism and establish their relevance in the context of the algebraic structures that are obeyed by the de Rham cohomological operators of differential geometry. In fact, our present field-theoretic system respects six continuous symmetry transformations and a couple of very useful discrete duality symmetry transformations. Out of the above six continuous symmetry transformations four are off-shell nilpotent (i.e. fermionic) in nature and two are bosonic. The algebraic structures, obeyed by the symmetry operators, are reminiscent of the algebra satisfied by the de Rham cohomological operators. Hence, our present $3D$ field-theoretic system provides a perfect example for Hodge theory where there is convergence of ideas from the physical aspects of the BRST formalism and mathematical ingredients that are connected with the cohomological operators of differential geometry at the algebraic level. One of the highlights of our present investigation is the appearance of a pseudo-scalar field in our theory (on the symmetry ground alone) which carries the negative kinetic term. Thus, it is one of the possible candidates for the ``phantom" fields of the cyclic, bouncing and self-accelerated cosmological models of the Universe., Comment: LaTeX file, 26 pages, v2: 30 pages, a few footnotes added, a new Appendix added, references expanded

We demonstrate the duality symmetry between the Abelian 1-form and 2-form basic gauge fields in the context of a three (2 + 1)-dimensional (3D) combined system of the field-theoretic model for the free Abelian 1-from and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism where the classical gauge-fixed Lagrangian density of this theory is generalized to its quantum counterpart as the BRST and co-BRST invariant Lagrangian density. We show clearly the existence of the off-shell nilpotent (co-)BRST symmetry transformations and establish their intimate connection through a set of underlying discrete duality symmetry transformations in our BRST-quantized theory. We briefly mention a bosonic symmetry transformation which is generated from the anticommutator of the above (co-)BRST symmetry transformations. We lay emphasis on the algebraic structures of the existing continuous as well as the discrete symmetry transformations in our theory (where they are treated as operators)., Comment: LaTeX file, 13 pages

We perform the constraint analysis of a three (2 + 1)-dimensional (3D) field-theoretic example for Hodge theory $(i)$ at the classical level within the ambit of Lagrangian formulation, and $(ii)$ at the quantum level within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We derive the conserved charges corresponding to the six continuous symmetries of our present theory. These six continuous summery transformations are the nilpotent (anti-)BRST and (anti-)co-BRST symmetries, a unique bosonic symmetry and the ghost-scale symmetry. It turns out that the Noether conserved (anti-)BRST charges are found to be non-nilpotent even though they are derived from the off-shell nilpotent versions of the continuous and infinitesimal (anti-)BRST symmetry transformations. We obtain the nilpotent versions of the (anti-)BRST charges from the non-nilpotent Noether (anti-)BRST charges and discuss the physicality criteria w.r.t. the latter to demonstrate that the operator forms of the first-class constraints (of the classical gauge theory) annihilate the physical states at the quantum level. This observation is consistent with Dirac's quantization conditions for the systems that are endowed with the constraints. We lay emphasis on the existence of a single (anti-)BRST invariant Curci-Ferrari (CF) type restriction in our theory and derive it from various theoretical angles., Comment: LaTeX file, 38 pages, version to appear in NPB

We focus on the continuous symmetry transformations for the three ($2 + 1$)-dimensional (3D) system of a combination of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We establish that this combined system is a tractable field-theoretic model of Hodge theory. The symmetry operators of our present theory provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. Our present investigation is important in the sense that, for the first time, we are able to establish an odd dimensional (i.e. $D = 3$) field-theoretic system to be an example for Hodge theory (besides earlier works on a few interesting ($0 + 1$)-dimensional toy models as well as a set of well-known ${\mathcal N} = 2$ SUSY quantum mechanical systems of physical interest). For the sake of brevity, we have not taken into account the 3D Chern-Simon term for the Abelian 1-form gauge field in our theory which allows the mass and gauge-invariance to co-exist together., Comment: LaTeX file, 14 pages, dedicated to the memory of Prof. C. P. Singh

We obtain the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations (corresponding to the infinitesimal classical gauge symmetry transformations) for the modified massive three $(2+1)$-dimensional (3D) Abelian 2-form gauge theory with a single pseudo-scalar field. The latter field (having the negative kinetic term and a well-defined mass) has already been shown (i) to exist in the modified version of the standard 3D St${\ddot u}$ckelberg formalism (on the solid mathematical grounds), (ii) to be a possible candidate for the ``phantom" field of some of the cosmological models of the Universe, and (iii) to be a possible candidate for dark matter. A couple of highlights of our present endeavor are (i) the observation that, even though the pseudo-scalar field does not transform under the gauge and (anti-)BRST symmetry transformations, it appears in the first-class constraints which annihilate the physical states at the quantum level, and (ii) the Noether conserved (anti-)BRST charges are found to be non-nilpotent. In our present investigation, we derive (i) the coupled (but equivalent) BRST and anti-BRST invariant Lagrangian densities, (ii) the conserved and off-shell nilpotent versions of the (anti-)BRST charges and the conserved ghost charge, (iii) the (anti-)BRST invariant Curci-Ferrari (CF) type restrictions, and (iv) the standard BRST algebra amongst the conserved and nilpotent (anti-)BRST charges and conserved ghost charge of our theory., Comment: LaTeX file, 33 pages v2: 34 pages, minor modifications in the title and text, references expanded

We present the largest optical photometry compilation of Gamma-Ray Bursts (GRBs) with redshifts ($z$). We include 64813 observations of 535 events (including upper limits) from 28 February 1997 up to 18 August 2023. We also present a user-friendly web tool \textit{grbLC} which allows users the visualization of photometry, coordinates, redshift, host galaxy extinction, and spectral indices for each event in our database. Furthermore, we have added a Gamma Ray Coordinate Network (GCN) scraper that can be used to collect data by gathering magnitudes from the GCNs. The web tool also includes a package for uniformly investigating colour evolution. We compute the optical spectral indices for 138 GRBs for which we have at least 4 filters at the same epoch in our sample and craft a procedure to distinguish between GRBs with and without colour evolution. By providing a uniform format and repository for the optical catalogue, this web-based archive is the first step towards unifying several community efforts to gather the photometric information for all GRBs with known redshifts. This catalogue will enable population studies by providing light curves (LCs) with better coverage since we have gathered data from different ground-based locations. Consequently, these LCs can be used to train future LC reconstructions for an extended inference of the redshift. The data gathering also allows us to fill some of the orbital gaps from Swift in crucial points of the LCs, e.g., at the end of the plateau emission or where a jet break is identified., Comment: 20 pages, 16 figures, 2 tables. Submitted to MNRAS, this version matches the third revision. The Online Materials and data will be available after the publication

We demonstrate the existence of a single pseudo-scalar (PS) field in the mathematically backed and parity preserving modifications of the standard St${\ddot u}$ckelberg formalism (SSF) in the context of the Lagrangian formulation of the (i) two (1 + 1)-dimensional (2D) massive Abelian 1-form gauge theory, (ii) three (2 + 1)-dimensional (3D) massive Abelian 2-form gauge theory, and (iii) four (3 + 1)-dimensional (4D) massive Abelian 3-form gauge theory. This PS field always turns-up with the (i) negative kinetic term, and (ii) higher order derivative terms. The latter terms are rendered into the well-defined terms due to the imposition of the on-shell condition for the PS field which is derived from the properly gauge-fixed Lagrangian densities for the above theories. These Lagrangian densities incorporate into themselves the (i) PS field with the negative kinetic term, and (ii) pure scalar field with the positive kinetic term. However, both these fields satisfy the Klein-Gordon (KG) equation of motion. The PS field (having the negative kinetic term and a well-defined mass) is one of the possible candidates for the ``phantom'' field which plays a crucial role in the cyclic, bouncing and self-accelerated cosmological models of the Universe. The ``exotic'' PS field also satisfies one of the criteria for being a possible candidate for dark matter, Comment: LaTeX file, 14 pages v2: 19 pages, major changes in the title and text, references expanded

On the basis of (i) the discrete and continuous symmetries (and corresponding conserved charges), (ii) the ensuing algebraic structures of the symmetry operators and conserved charges, and (iii) a few basic concepts behind the subject of differential geometry, we show that the celebrated Friedberg-Lee-Pang-Ren (FLPR) quantum mechanical model (describing the motion of a single non-relativistic particle of unit mass under the influence of the general spatial 2D rotationally invariant potential) provides a tractable physical example for the Hodge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism where the symmetry operators and conserved charges lead to the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. We concisely mention the Hodge decomposition theorem in the quantum Hilbert space of states and choose the harmonic states as the real physical states of our theory. We discuss the physicality criteria w.r.t. the conserved and nilpotent versions of the (anti-)BRST and (anti-)co-BRST charges and the physical consequences that ensue from them., Comment: LaTeX file, 30 pages, dedicated to the memory of Prof. O. N. Srivastava, version to appear in AoP

We demonstrate the existence of a set of novel off-shell nilpotent and absolutely anticommuting continuous symmetry transformations, within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, which are over and above the usual off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations that are respected by the first-order Lagrangian for the Friedberg-Lee-Pang-Ren (FLPR) model that describes the motion of a non-relativistic particle of unit mass moving under the influence of a general rotationally invariant spatial two-dimensional potential. We christen these novel set of fermionic symmetry transformations as the (anti-)co-BRST symmetry transformations because the gauge-fixing term remains invariant under them. We derive the conserved and off-shell nilpotent (anti-)BRST and (anti-)co-BRST charges and comment on the physicality criteria w.r.t. them where we establish the presence of the operator forms of the first-class constraints (of the original classical gauge theory) at the quantum level., Comment: LaTeX file, 12 pages, version to appear in EPL

We demonstrate that the generators for the local, continuous and infinitesimal classical gauge symmetry transformations in the cases of (i) the St$\ddot u$ckelberg-modified massive Abelian 1-form and 2-form theories, and (ii) the massless Abelian 1-form and 2-form free theories owe their origin to the first-class constraints of the these theories. We establish a connection between the standard forms of the generators and the Noether conserved charges for the modified massive and massless versions of the above theories. We discuss the appearance of these constraints, within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, through the physicality criteria w.r.t. the conserved and nilpotent (anti-)BRST charges. One of the highlights of our present investigation is the observation that, in the context of the modified massive and massless Abelian 2-form theories, the modified forms of the standard Noether (anti-)BRST charges are required which are found to be off-shell nilpotent and they lead to the appearance of the operator forms of the first-class constraints through the physicality criteria at the quantum level. We also comment on (i) the existence of the Curci-Ferrari (CF)-type restrictions on the Abelian 2-form theories (with and without mass), (ii) the modifications in the St$\ddot u$ckelberg-technique for the massive 2D Abelian 1-form and 4D Abelian 2-form theories and their consequences, and (iii) the off-shell nilpotent version of the conserved co-BRST charge and its role in the physicality criteria for the St$\ddot u$ckelberg-modified 4D massive Abelian 2-form theory., Comment: LaTeX file, 45 pages, dedicated to the memory of Prof. G. Rajasekaran

We demonstrate the existence of the first-class constraints on the massless Abelian 3-form theory which generate the classical gauge symmetry transformations for this theory in any arbitrary D-dimension of spacetime. We write down the explicit expression for the generator in terms of these first-class constraints. Using the celebrated Noether theorem, corresponding to the gauge symmetry transformations, we derive the Noether conserved current and conserved charge. The latter is connected with the first-class constraints of the theory in a subtle manner as we demonstrate clearly in our present investigation. We comment on the first-class constraints within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism where the conserved (anti-)BRST charges are the generalizations of the above generator for the classical gauge symmetry transformation. The standard Noether conserved (anti-)BRST charges are found to be non-nilpotent. We derive the nilpotent versions of the (anti-)BRST charges. One of the interesting observations of our present endeavor is the result that only the nilpotent versions of the conserved (anti-)BRST charges lead to the annihilation of the physical states by the operator form of the first-class constraints at the quantum level which is consistent with the Dirac quantization condition for the systems that are endowed with any kind of constraints. We comment on the existence of the Curci-Ferrari (CF) type restrictions from different theoretical angles, too., Comment: LaTeX file, 28 pages, journal reference given. arXiv admin note: text overlap with arXiv:2207.11738

In this brief review-cum-research article, we discuss a few key aspects of the off-shell nilpotent (anti-)BRST symmetry transformations, Curci-Ferrari (CF) type restriction(s), coupled Lagrangians/Lagrangian densities, etc., for the 1D diffeomorphism (i.e. reparameterization) invariant models of $(i)$ a non-relativistic and non-SUSY free particle, $(ii)$ a scalar (i.e. non-SUSY) relativistic free particle, $(iii)$ a spinning (i.e. SUSY) relativistic free particle, and $(iv)$ a 2D diffeomorphism invariant model of a specific bosonic string theory within the framework of BRST and related supervariable/superfield approach. We take up a new 1D diffeomorphism invariant model of an interacting scalar relativistic particle with the electromagnetic field. The latter is treated as a constant background variable and is, therefore, independent of the evolution parameter. We show that the universal nature of the CF-type restriction is maintained in the case of this new model, too. We exploit the modified Bonora-Tonin supervariable/superfield approach (MBTSA) to BRST formalism in the context of the 1D and 2D diffeomorphism invariant theories to prove the universal nature of the CF-type restriction(s). We further demonstrate that the 1D diffeomorphism invariant models of all kinds of particles are described by the singular Lagrangians. This singular nature has, to the best of our knowledge, not been explicitly shown elsewhere. Thus, these 1D models also respect the gauge symmetry transformations which are generated by the first-class constraints that exist on them. The equivalence of the 1D diffeomorphism and gauge symmetries is also established under specific conditions.., Comment: LaTeX file, 45 pages, minor typos fixed, journal reference given

In some of the physically interesting gauge systems, we show that the application of the Noether theorem does not lead to the deduction of the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST charges that obey precisely the off-shell nilpotency property despite the fact that these charges are $(i)$ derived by using the off-shell nilpotent (anti-)BRST symmetry transformations, $(ii)$ the generators of the above continuous symmetry transformations, and $(iii)$ conserved w.r.t. the time-evolution due to the Euler-Lagrange equations of motion derived from the Lagrangians/Lagrangian densities (that describe the dynamics of the suitably chosen physical systems). We propose a systematic method for the derivation of the off-shell nilpotent (anti-)BRST charges from the corresponding {non-nilpotent Noether conserved (anti-)BRST charges. To corroborate the sanctity and preciseness of our proposal, we take into account the examples of $(i)$ the one ($0 + 1$)-dimensional (1D) system of a massive spinning (i.e. SUSY) relativistic particle, $(ii)$ the D-dimensional non-Abelian 1-form gauge theory, and $(iii)$ the Abelian 2-form and the St${\ddot u}$ckelberg-modified version of the massive Abelian 3-form gauge theories in any arbitrary D-dimension of spacetime. Our present endeavor is a brief review where some decisive proposals have been made and a few novel results have been obtained as far as the nilpotency property is concerned., Comment: LaTeX file, 35 pages, version to appear in UNIVERSE

For the St$\ddot u$ckelberg-modified massive Abelian 3-form theory in any arbitrary D-dimension of spacetime, we show that its classical gauge symmetry transformations are generated by the first-class constraints. We establish that the Noether conserved charge (corresponding to the local gauge symmetry transformations) is same as the standard form of the generator for the underlying local gauge symmetry transformations (expressed in terms of the first-class constraints). We promote these classical local, continuous and infinitesimal gauge symmetry transformations to their quantum counterparts Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations which are respected by the coupled (but equivalent) Lagrangian densities. We derive the conserved (anti-)BRST charges by exploiting the theoretical potential of Noether's theorem. However, these charges turn our to be non-nilpotent. Some of the highlights of our present investigation are (i) the derivation of the off-shell nilpotent versions of the (anti-)BRST charges from the standard non-nilpotent Noether conserved (anti-)BRST charges, (ii) the appearance of the operator forms of the first-class constraints at the quantum level through the physicality criteria w.r.t. the nilpotent versions of the (anti-)BRST charges, and (iii) the deduction of the CF-type restrictions from the straightforward equality of the coupled (anti-)BRST invariant Lagrangian densities as well as from the requirement of the absolute anticommutativity of the off-shell nilpotent versions of the (anti-)BRST charges., Comment: LaTeX file, 47 pages, one table, version to appear in Journal of Mathematical Physics

Using element-specific measurements of the ultrafast demagnetization of Ru/Fe$_{65}$Co$_{35}$ heterostructures, we show that Ru can exhibit a significant magnetic contrast (3% asymmetry) resulting from ultrafast spin currents emanating from the demagnetization process of the FeCo layer. We use this magnetic contrast to investigate how superdiffusive spin currents are affected by the doping of heavy elements in the FeCo layer. We find that the spin currents are strongly suppressed, and that the recovery process in Ru slows down, by Re doping. This is in accordance with a change in interface reflectivity of spin currents as found by the superdiffusive spin transport model., Comment: 7 pages, 5 figures

We derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for any arbitrary D-dimensional St$\ddot u$ckelberg-modified massive Abelian 3-form theory within the framework of augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism where, in addition to the horizontality condition (HC), we exploit the theoretical strength of the gauge invariant restriction (GIR) to deduce the proper transformations for the gauge, associated (anti-)ghost fields, auxiliary fields, St$\ddot u$ckelberg compensating field, etc. In fact, it is an elegant and delicate combination of HC and GIR (within the ambit of AVSA) that is crucial for all our discussions and derivations. One of the highlights of our present endeavor is the deduction of a new set of (anti-)BRST invariant Curci-Ferrari (CF)-type restrictions which are not found in the massless version of our present theory where only the HC plays an important role in the derivation of all the (anti-)BRST transformations and a very specific set of CF-type restrictions. The alternative ways of the derivation of the full set of the latter, from various theoretical considerations, are also interesting results of our present investigation., Comment: LaTeX file, 40 pages, one figure, journal version

We demonstrate that the celebrated St$\ddot u$ckelberg formalism gets modified in the case of a massive four (3+1)-dimensional (4D) Abelian 2-form theory due to the presence of a self-duality discrete symmetry in the theory. The latter symmetry entails upon the modified 4D massive Abelian 2-form gauge theory to become a massive model of Hodge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism where there is existence of a set of (anti-)co-BRST transformations corresponding to the usual nilpotent (anti-)BRST transformations. The latter exist in any arbitrary dimension of spacetime for the usual St$\ddot u$ckelberg-modified massive Abelian 2-form gauge theory. The modification in the St$\ddot u$ckelberg technique is backed by the precise mathematical arguments from the differential geometry where the exterior derivative and Hodge duality operator play the decisive roles. The modified version of the St$\ddot u$ckelberg technique remains invariant under the discrete duality transformations which also establish a precise and deep connection between the off-shell nilpotent (anti-)BRST and (anti-)co-BRST transformations. We have clarified a simple trick to get rid of the higher derivative terms in the appropriate Lagrangian densities so that our 4D theory can become consistent and renormalizable., Comment: LaTeX file, 28 pages, version to appear in UNIVERSE (2023); dedicated to the memory of Prof. T. Pradhan

We demonstrate that the standard Stueckelberg-modified Proca theory (i.e. a massive Abelian 1-form theory) respects the classical gauge and corresponding quantum (anti-)BRST symmetry transformations in any arbitrary dimension of spacetime within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We further show that the Stueckelberg formalism gets modified in the two (1+1)-dimensions of spacetime due to a couple of discrete duality symmetries in the theory which turn out to be responsible for the existence of the nilpotent (anti-)co-BRST symmetry transformations corresponding to the nilpotent (anti-)BRST symmetry transformations of our theory. These nilpotent symmetries exist together in the modified version of the two (1+1)-dimensional (2D) Proca theory. We provide the mathematical basis for the modification of the Stueckelberg-technique, the existence of the discrete duality as well as the continuous (anti-)co-BRST symmetry transformations in the 2D modified version of Proca theory., Comment: LaTeX file, 13 pages, minor changes in the text, journal reference given

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of the BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess-Zumino terms, for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well., Comment: 56 pages, typos corrected, bibliography completed, to appear in "Universe"

We take up the St${\ddot u}$ckelberg-modified version of the two (1+1)-dimensional (2D) Proca theory, in interaction with the Dirac fields, to study its various continuous and discrete symmetry transformations and show that this specific interacting 2D field-theoretic model provides a tractable example for the Hodge theory because its symmetries (and corresponding conserved charges) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. The physical state of this theory is chosen to be the harmonic state (of the Hodge decomposed state) in the quantum Hilbert space which is annihilated by the conserved and nilpotent (anti-)BRST as well as (anti-)co-BRST charges. A physical consequence of this study is an observation that the 2D anomaly, at the quantum level, does not lead to any problem as far as the consistency and unitarity of our present 2D theory is concerned. In other words, our present 2D field-theoretic model is amenable to particle interpretation despite the presence of the local chiral symmetry (which is associated with the nilpotent (anti-)co-BRST symmetry transformations) besides the presence of the nilpotent (anti-)BRST symmetries (which are connected with the local gauge symmetry). The physicality condition with the (anti-)co-BRST charges implies that the 2D anomaly term is trivial in our present theory. Hence, our 2D theory is consistent, unitary and amenable to particle interpretation., Comment: LaTeX file, 27 pages, no figures

Exploiting the theoretical potential of the modified Bonora-Tonin superfield approach (MBTSA) as well as the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the complete set of off-shell nilpotent (anti-)BRST symmetry transformations corresponding to the classical two $(1 + 1)$-dimensional (2D) diffeomorphism symmetry transformations on the world-sheet (that is traced out by the motion of a model of bosonic string). Only the BRST symmetry transformations for this model have been discussed in the earlier literature. We derive the (anti-)BRST invariant Curci-Ferrari (CF) type restrictions (using MBTSA) which turn out to be the root-cause behind the absolute anticommutativity of the above (anti-)BRST symmetry transformations. We capture the symmetry invariance of the (anti-)BRST invariant Lagrangian densities within the ambit of ACSA. The derivation of the proper anti-BRST transformations (corresponding to the already known BRST transformations) and the (anti-)BRST invariant CF-type restrictions are the novel results in our present endeavor., Comment: LaTeX file, 22 pages, minor corrections in the text, references in journal style

We exploit the theoretical strength of the supervariable and Becchi-Rouet-Stora-Tyutin (BRST) formalisms to derive the proper (i.e. off-shell nilpotent and absolutely anticommuting) (anti-)BRST symmetry transformations for the reparameterization invariant model of a non-relativistic (NR) free particle whose space $(x)$ and time $(t)$ variables are function of an evolution parameter $(\tau)$. The infinitesimal reparameterization (i.e. 1D diffeomorphism) symmetry transformation of our theory is defined w.r.t. this evolution parameter $(\tau)$. We apply the modified Bonora-Tonin (BT) supervariable approach (MBTSA) as well as the (anti-)chiral supervariable approach (ACSA) to BRST formalism to discuss various aspects of our present system. For this purpose, our 1D ordinary theory (parameterized by $\tau$) is generalized onto a $(1, 2)$-dimensional supermanifold which is characterized by the superspace coordinates $Z^M = (\tau, \theta, \bar\theta)$ where a pair of Grassmannian variables satisfy the fermionic relationships: $\theta^2 = {\bar\theta}^2 = 0, \, \theta\,\bar\theta + \bar\theta\,\theta = 0$ and $\tau$ is the bosonic evolution parameter. In the context of ACSA, we take into account only the (1, 1)-dimensional (anti-)chiral super sub-manifolds of the general (1, 2)-dimensional supermanifold. The derivation of the universal Curci-Ferrari (CF)-type restriction, from various underlying theoretical methods, is a novel observation in our present endeavor. Furthermore, we note that the form of the gauge-fixing and Faddeev-Popov ghost terms for our NR and non-SUSY system is exactly same as that of the reparameterization invariant SUSY (i.e. spinning) and non-SUSY (i.e. scalar) relativistic particles. This is a novel observation, too., Comment: LaTeX file, 31 pages, Version to appear in AHEP (2021)

We carry out the Becchi-Rouet-Stora-Tyutin (BRST) quantization of the one (0 + 1)-dimensional (1D) model of a free massive spinning relativistic particle (i.e. a supersymmetric system) by exploiting its classical infinitesimal and continuous reparameterization symmetry transformations. We use the modified Bonora-Tonin (BT) supervariable approach (MBTSA) to BRST formalism to obtain the nilpotent (anti-)BRST symmetry transformations of the target space variables and the (anti-)BRST invariant Curci-Ferrari (CF)-type restriction for the 1D model of our supersymmetric (SUSY) system. The nilpotent (anti-)BRST symmetry transformations for other variables of our model are derived by using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of the latter, we have shown the existence of the CF-type restriction by proving the (i) symmetry invariance of the coupled Lagrangians, and (ii) the absolute anticommutativity property of the conserved (anti-)BRST charges. The application of the MBTSA to a physical SUSY system (i.e. a 1D model of a massive spinning particle) is a novel result in our present endeavor. In the application of ACSA, we have considered only the (anti-)chiral super expansions of the supervariables. Hence, the observation of the absolute anticommutativity of the (anti-)BRST charges is a novel result. The CF-type restriction is universal in nature as it turns out to be the same for the SUSY and non-SUSY reparameterization (i.e. 1D diffeomorphism) invariant models of the (non-)relativistic particles., Comment: LaTeX file, 38 pages, version to appear in AHEP. arXiv admin note: text overlap with arXiv:2006.07874

We discuss the continuous and infinitesimal gauge, supergauge, reparameterization, nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries and derive corresponding nilpotent charges for the one (0+1)-dimensional (1D) massive model of a spinning relativistic particle. We exploit the theoretical potential and power of the BRST and supervariable approaches to derive the (anti-)BRST symmetries and coupled (but equivalent) Lagrangians for this system. In particular, we capture the off-shell nilpotency and absolute anticommutatvity of the conserved (anti-)BRST charges within the framework of the newly proposed (anti-)chiral supervariable approach (ACSA) to BRST formalism where only the (anti-)chiral supervariables (and their suitable super expansions are taken into account along the Grassmannian direction(s)). One of the novel observations of our present investigation is the derivation of the Curci-Ferrari (CF)-type restriction by the requirement of the absolute anticommutatvity of the (anti-)BRST charges in the ordinary space. We obtain the same restriction within the framework of ACSA to BRST formalism by (i) the symmetry invariance of the coupled Lagrangians, and (ii) the proof of the absolute anticommutatvity of the conserved and nilpotent (anti-)BRST charges. The observation of the anticommutativity property of the (anti-)BRST charges is a novel result in view of the fact that we have taken into account only the (anti-)chiral super expansions., Comment: LaTeX file, 38 pages, version to appear in AHEP

We report on optically induced, ultrafast magnetization dynamics in the Heusler alloy $\mathrm{Co_{2}FeAl}$, probed by time-resolved magneto-optical Kerr effect. Experimental results are compared to results from electronic structure theory and atomistic spin-dynamics simulations. Experimentally, we find that the demagnetization time ($\tau_{M}$) in films of $\mathrm{Co_{2}FeAl}$ is almost independent of varying structural order, and that it is similar to that in elemental 3d ferromagnets. In contrast, the slower process of magnetization recovery, specified by $\tau_{R}$, is found to occur on picosecond time scales, and is demonstrated to correlate strongly with the Gilbert damping parameter ($\alpha$). Our results show that $\mathrm{Co_{2}FeAl}$ is unique, in that it is the first material that clearly demonstrates the importance of the damping parameter in the remagnetization process. Based on these results we argue that for $\mathrm{Co_{2}FeAl}$ the remagnetization process is dominated by magnon dynamics, something which might have general applicability.

We derive the off-shell nilpotent (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the four (3+1)-dimensional (4D) St$\ddot{u}$ckelberg-modified massive Abelian 2-form gauge theory. We perform exactly similar kind of exercise for the derivation of the off-shell nilpotent (anti-)co-BRST symmetry transformations, too. In the above derivations, the symmetry invariant restrictions on the superfields play very important and decisive roles. To prove the sanctity of the above nilpotent symmetries, we generalize our 4D ordinary theory (defined on the 4D flat Minkowskian spacetime manifold) to its counterparts (4,1)-dimensional (anti-)chiral super sub-manifolds of the (4,2)-dimensional supermanifold which is parameterized by the superspace coordinates $Z^{M} = (x^{\mu},\theta, \bar{\theta} ) $ where $x^\mu ( \mu = 0,1,2,3 )$ are the bosonic coordinates and a pair of Grassmannian variables $(\theta, \bar{\theta})$ are fermionic: ($\theta^{2} = \bar{\theta^{2}} = 0, \,\,\theta\,\bar{\theta} +\bar{\theta}\,\theta = 0$) in nature. One of the novel observations of our present endeavor is the derivation of the Curci-Ferrari (CF) type restrictions from the requirement of the symmetry invariance of the coupled (but equivalent) Lagrangian densities for our theory within the framework of ACSA to BRST formalism. We also exploit the standard techniques of ACSA to capture the off-shell nilpotency and absolute anticommutativity of the conserved (anti-)BRST as well as the (anti-)co-BRST charges. In a subtle manner, the proof of the absolute anticommutativity of the above conserved charges also implies the existence of the appropriate CF-type restrictions on our theory., Comment: LaTeX file, 55 pages, minor changes in the title and text, version to appear in IJMPA

We apply the supervariable approach to derive the proper quantum Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries for the 1D diffeomorphism invariant model of a free scalar relativistic particle by exploiting the infinitesimal classical reparameterization (i.e. 1D diffeomorphism) symmetry of this theory. We derive the conserved and off-shell nilpotent (anti-)BRST charges and prove their absolute anticommutativity property by using the virtues of Curci-Ferrari (CF)-type restriction of our present theory. We establish the sanctity of the existence of CF-type restriction (i) by considering the (anti-)BRST symmetry transformations of the coupled (but equivalent) Lagrangians, and (ii) by proving the symmetry invariance of the Lagrangians within the framework of supervariable approach. We capture the nilpotency and absolute anticommutativity of the conserved (anti-)BRST charges within the framework of (anti-)chiral supervariable approach (ACSA) to BRST formalism. One of the novel observations of our present endeavor is the derivation of CF-type restriction by using the modified Bonora-Tonin (BT) supervariable approach (while deriving the (anti-)BRST symmetries for the target spacetime and/or momenta variables) and by symmetry considerations of the Lagrangians of the theory. The rest of the (anti-)BRST symmetries, for the other variables, are derived by using the newly proposed ACSA. We also demonstrate the existence of CF-type restriction in the proof of absolute anticommutativity of the (anti-)BRST charges., Comment: LaTeX file, 29 pages, minor modifications in the title and text, references expanded, version to appear in IJMPA

The magneto-optical response of Fe and Ni during ultrafast demagnetization is studied experimentally and theoretically. We have performed pump-probe experiments in the transverse magneto-optical Kerr effect (T-MOKE) geometry using photon energies that cover the M-absorption edges of Fe and Ni between 40 to 72 eV. The asymmetry was detected by measuring the reflection of light for two different orientations of the sample magnetization. Density functional theory (DFT) wasused to calculate the magneto-optical response of different magnetic configurations, representing different types of excitations: long-wavelength magnons, short wavelength magnons, and Stoner excitations. In the case of Fe, we find that the calculated asymmetry is strongly dependent on the specific type of magnetic excitation. Our modelling also reveals that during remagnetization Fe is, to a reasonable approximation, described by magnons, even though small non-linear contributions could indicate some degree of Stoner excitations as well. In contrast, we find that the calculated asymmetry in Ni is rather insensitive to the type of magnetic excitations. However, there is a weak non-linearity in the relation between asymmetry and the off-diagonal component of the dielectric tensor, which does not originate from the modifications of the electronic structure. Our experimental and theoretical results thus emphasize the need of considering a coupling between asymmetry and magnetization that may be more complex that a simple linear relationship. This insight is crucial for the microscopic interpretation of ultrafast magnetization experiments.

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) approach, we discuss mainly the fermionic (i.e. off-shell nilpotent) (anti-)BRST, (anti-)co-BRST and some discrete dual-symmetries of the appropriate Lagrangian densities for a two (1+1)-dimensional (2D) modified Proca (i.e. a massive Abelian 1-form) theory without any interaction with matter fields. One of the novel observations of our present investigation is the existence of some kinds of restrictions in the case of our present St\"{u}ckelberg-modified version of the 2D Proca theory which is not like the standard Curci-Ferrari (CF)-condition of a non-Abelian 1-form gauge theory. Some kinds of similarities and a few differences between them have been pointed out in our present investigation. To establish the sanctity of the above off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetries, we derive them by using our newly proposed (anti-)chiral superfield formalism where a few specific and appropriate sets of invariant quantities play a decisive role. We express the (anti-)BRST and (anti-)co-BRST conserved charges in terms of the superfields that are obtained after the applications of (anti-)BRST and (anti-)co-BRST invariant restrictions and prove their off-shell nilpotency and absolute anticommutativity properties, too. Finally, we make some comments on (i) the novelty of our restrictions/obstructions, and (ii) the physics behind the negative kinetic term associated with the pseudo-scalar field of our present theory., Comment: LaTeX file, 58 pages, Journal reference given