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Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are commutative finite flat algebras over the cohomology of the classifying space of the group. They are isomorphic with the equivariant intersection cohomology of affine Schubert varieties, endowing the latter with a new ring structure. Study of the finer aspects of the structure of the big algebras will also furnish the stalks of the intersection cohomology with ring structure, thus ringifying Lusztig's q-weight multiplicity polynomials i.e., certain affine Kazhdan-Lusztig polynomials. [ABSTRACT FROM AUTHOR]

In [11], Hausel introduced a commutative algebra — the multiplicity algebra — associated to a fixed point of the C ∗ -action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relations in the algebra are described by a family of quadrics and we focus on the discriminant of this family, providing a new viewpoint on the moduli space of stable bundles. The discriminant in our examples demonstrates that as the bundle varies, we obtain a continuous variation in the isomorphism class of the algebra. [ABSTRACT FROM AUTHOR]

We study the Einstein-Yang-Mills-Higgs (EYMH) system with a positive cosmological constant in the Bianchi type I space-time with locally rotational symmetry (LRS). In particular, we consider the nonlinear interaction of the Higgs field with the Yang-Mills field coupled to an unknown gravitational field. For the considered model, from certain additional conditions (the temporal gauge and some symmetries), we derive the conservation laws for the field equations and we then deduce the exact formulation of equations in the geometric framework. Furthermore, using an iterative approch and some mathematical analysis tools, we study the above system of equations. We then establish a global existence result for the homogeneous solution and we analyse its asymptotic behaviour. [ABSTRACT FROM AUTHOR]

Extending previous results, we explore aspects of the reheating mechanism for non-minimal Higgs inflation in the strong coupling regime. We constrain the radiative corrections for the inflaton's potential by considering the Coleman-Weinberg approximation and use the Renormalization Group Equations for the Higgs field to derive an upper limit on the top quark mass. Using the current Cosmic Microwave Background, Baryon Acoustic Oscillation, and Supernovae data, we obtain mt≤170.44 GeV, confirming the observational compatibility of the model with recent mt estimates reported by the CMS collaboration. We also analyze the breakdown of the well-known correlation involving the Hubble constant H0 and the clustering parameter σ8, which makes the model interesting in light of the cosmological tensions discussed over the last decade.

A mathematical model is formulated for the evolution of plane perturbations in a cosmological two-component statistical system of completely degenerate scalarly charged fermions with an asymmetric scalar Higgs interaction. A complete closed system of differential equations are constructed to describe the unperturbed state of a homogeneous and isotropic system and a system of self-consistent evolution equations of small perturbations. [ABSTRACT FROM AUTHOR]

A geometric quantization using a partial differential equation version of topological recursion is established for the compactified cotangent bundle of a smooth projective curve of an arbitrary genus. In this quantization, the Hitchin spectral curve of a rank 2 meromorphic Higgs bundle on the base curve corresponds to a quantum curve, which is a Rees D-module on the base. The topological recursion then gives an all-order asymptotic expansion of its solution, thus determining a state vector corresponding to the spectral curve as a meromorphic Lagrangian. We propose a generalization of the topological recursion for a singular spectral curve. We show that the PDE version of the topological recursion automatically selects the normal ordering of the canonical coordinates, and determines the unique quantization of the spectral curve. The quantum curve thus constructed has the semi-classical limit that agrees with the original spectral curve. Typical examples of our construction includes classical differential equations, such as Airy, Hermite, and Gauß hypergeometric equations. The topological recursion gives an asymptotic expansion of solutions to these equations at their singular points, relating Higgs bundles and various quantum invariants.

This contribution sets out to present an advanced topic of major relevance in Physics: the spontaneous symmetry breaking, a crucial issue for the Higgs Mechanism, in a suitable approach for the high school level. The mathematical model of symmetry breaking is approached by exploiting the analogy between the simple harmonic and anharmonic oscillators. Next, we discuss how the Higgs boson's physical mass arises from the oscillation of the Higgs oscillatory coordinate, here playing the role of the Higgs field. We also propose the use of a computer simulation, with the Modellus software, to compute the energy of the oscillators. The purpose of carrying out simulation is to render the learning process more efficient and to increase the action of the student. [ABSTRACT FROM AUTHOR]

A generalization of the original Bargmann–Wigner equations for spin-1 massive fields is employed, taking fully into account all internal degrees of freedom associated with the underlying chiral bases of the constituent spin-1/2 representations. Through the specification of a chiral basis, the chiral Bargmann–Wigner equations are reduced to a Proca-like form coupled by chirality to an auxiliary equation for a spin-0 massive field. The coupling derived is a new phenomenon whose physical implications are discussed in the context of identification of this field with the Higgs field and dark matter. [ABSTRACT FROM AUTHOR]

We introduce the moduli space of quasi-parabolic SL(2,C)-Higgs bundles over a compact Riemann surface Σ and consider a natural involution, studying its fixed point locus when Σ is C P1 and establishing an identification with a moduli space of null polygons in Minkowski 3-space. [ABSTRACT FROM AUTHOR]

A complete model of cosmological evolution of a classical scalar field with the Higgs potential is studied and simulated on a computer without assumption that the Hubble constant is nonnegative. The corresponding dynamical system is qualitatively analyzed and the Einstein–Higgs hypersurfaces the topology of which determines the global properties of the phase trajectories of the cosmological model are classified. [ABSTRACT FROM AUTHOR]

Previously we have shown that the algebra J 3 [ C ⊗ O ] ⊗ C ℓ (4 , C) , given by the tensor product of the complex exceptional Jordan J 3 [ C ⊗ O ] and the complex Clifford algebra C ℓ (4 , C) , can describe all of the spinorial degrees of freedom of three generations of fermions in four-space-time dimensions. We extend our construction to show that it also includes the degrees of freedom of three sets of pairs of complex scalar Higgs-doublets { H L (m) , H R (m) } ; m = 1 , 2 , 3 , and their CPT conjugates. Furthermore, a close inspection of the fermion structure of each generation reveals that it fits naturally with the sixteen complex-dimensional representation of the internal left/right symmetric gauge group G LR = SU (3) C × SU (2) L × SU (2) R × U (1) . It is reviewed how the latter group emerges from the intersection of SO (10) and SU (3) × SU (3) × SU (3) in E 6 . In the concluding remarks we briefly discuss the role that the extra Higgs fields may have as dark matter candidates; the construction of Chern–Simons-like matrix cubic actions; hexaquarks; supersymmetry and Clifford bundles over the complex-octonionic projective plane (C ⊗ O) P 2 whose isometry group is E 6 . [ABSTRACT FROM AUTHOR]

Extending previous results, we explore aspects of the reheating mechanism for non-minimal Higgs inflation in the strong coupling regime. We constrain the radiative corrections for the inflaton's potential by considering the Coleman-Weinberg approximation and use the Renormalization Group Equations for the Higgs field to derive an upper limit on the top quark mass. Using the current Cosmic Microwave Background, Baryon Acoustic Oscillation, and Supernovae data, we obtain m t ≤ 170.44 GeV, confirming the observational compatibility of the model with recent m t estimates reported by the CMS collaboration. We also analyze the breakdown of the well-known correlation involving the Hubble constant H 0 and the clustering parameter σ 8 , which makes the model interesting in light of the cosmological tensions discussed over the last decade. [ABSTRACT FROM AUTHOR]

The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and nondiagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants. We study the harmonic oscillator with the interacting potential, λ 1 x 4 / 6 + λ 2 x 6 / 1 2 0 , where λ 1 and λ 2 are coupling constants, and x is the position operator. In this study, each perturbed term has an exact solution. We demonstrate the accurate study of the spectrum and 〈 x 2 〉 up to the next leading-order correction. In particular, we study a similar problem of Higgs field from the inverted mass term to demonstrate the possible nontrivial application of particle physics. [ABSTRACT FROM AUTHOR]

The composition algebra based methodology (CAM) (Wolk in Pap Phys 9:090002, 2017, Phys Scr 94:025301, 2019, Adv Appl Clifford Algebras 27(4):3225, 2017, J Appl Math Phys 6:1537, 2018, Phys Scr 94:105301, 2019) has previously been shown to generate the pre-Higgs Standard Model Lagrangian. In this paper the symmetry of general covariance is incorporated into CAM. The Riemann curvature tensor thereby arises, from which gravity-field Lagrangians are constructed. A Higgs-like scalar field coupled to the spacetime metric tensor also manifests. [ABSTRACT FROM AUTHOR]

Abstract In the context of the Higgs model involving gauge and Yukawa interactions with the spontaneous gauge symmetry breaking, we consider $$\lambda \phi ^4$$ λ ϕ 4 inflation with non-minimal gravitational coupling, where the Higgs field is identified as the inflaton. Since the inflaton quartic coupling is very small, once quantum corrections through the gauge and Yukawa interactions are taken into account, the inflaton effective potential most likely becomes unstable. In order to avoid this problem, we need to impose stability conditions on the effective inflaton potential, which lead to not only non-trivial relations amongst the particle mass spectrum of the model, but also correlations between the inflationary predictions and the mass spectrum. For concrete discussion, we investigate the minimal $$B-L$$ B - L extension of the standard model with identification of the $$B-L$$ B - L Higgs field as the inflaton. The stability conditions for the inflaton effective potential fix the mass ratio amongst the $$B-L$$ B - L gauge boson, the right-handed neutrinos and the inflaton. This mass ratio also correlates with the inflationary predictions. In other words, if the $$B-L$$ B - L gauge boson and the right-handed neutrinos are discovered in the future, their observed mass ratio provides constraints on the inflationary predictions.

We consider an extension of the standard model based on the group U (2) × U (3) , which is naturally compatible with the standard model interacting-particle representations and the spontaneous symmetry breaking of U (2) × U (3) to an electrostrong U (3). In its minimal version, the model only adds one extra U (1) gauge boson and it implies that the hypercharge is distributed between the factors of the hyperweak and hyperstrong forces. We show that the anomaly cancellation condition can be solved by adding exotic fermions associated with a 16-dimensional representation of U (2) × U (3). A brief discussion of the mechanism of the spontaneous breakdown of U (2) × U (3) in the gauge boson sector is given. [ABSTRACT FROM AUTHOR]

Scalar fields describe interesting phenomena such as Higgs bosons, dark matter and dark energy, and are found to be quite common in physical theories. These fields are susceptible to gravitational forces so that being massless is not enough to remain conformal invariant. They should also be connected directly to the scalar curvature. Because of this characteristics, we investigated the structure and interactions of scalar fields under the conformal transformations. We show how to reduce the quadratic quantum contributions in the single scalar field theory. In the multi-scalar field theories, we analyzed interactions in certain limits. We suggest a new method for stabilizing Higgs bosons. [ABSTRACT FROM AUTHOR]

We discuss the possibility that dark matter corresponds to an oscillating scalar field coupled to the Higgs boson. We argue that the initial field amplitude should generically be of the order of the Hubble parameter during inflation, as a result of its quasi-de Sitter fluctuations. This implies that such a field may account for the present dark matter abundance for masses in the range 10−6–10−4eV, if the tensor-to-scalar ratio is within the range of planned CMB experiments. We show that such mass values can naturally be obtained through either Planck-suppressed non-renormalizable interactions with the Higgs boson or, alternatively, through renormalizable interactions within the Randall–Sundrum scenario, where the dark matter scalar resides in the bulk of the warped extra-dimension and the Higgs is confined to the infrared brane.