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We show that the ideas related to integrability and symmetry play an important role not only in the string T-duality story but also in its point particle counterpart. Applying those ideas, we find that the T-duality seems to be a more widespread phenomenon in the context of the point particle dynamics than it is in the string one; moreover, it concerns physically very relevant point particle dynamical systems and not just somewhat exotic ones fabricated for the purpose. As a source of T-duality examples, we consider maximally superintegrable spherically symmetric electro-gravitational backgrounds in n dimensions. We then describe in detail four such spherically symmetric dynamical systems which are all mutually interconnected by a web of point particle T-dualities. In particular, the dynamics of a charged particle scattered by a repulsive Coulomb potential in a flat space is T-dual to the dynamics of the Coulomb scattering in the space of constant negative curvature, but it is also T-dual to the (conformal) Calogero–Moser inverse square dynamics both in flat and hyperbolic spaces. Thus knowing just the Hamiltonian dynamics of the scattered particle cannot give us information about the curvature of the space in which the particle moves. [ABSTRACT FROM AUTHOR]

We compute the conserved charges associated with the asymptotic symmetries of massless particles by examining their free theory in Minkowski space–time. We give a procedure to systematically deduce the fall off of the massless fields at spatial infinity and show that it has a universal behavior when expressed in tangent space. We do this for generic massless particles. We do not impose gauge fixing conditions, which will allow us to uncover new nonzero charges for the graviton beyond the well-known supertranslation charges. We also compute conserved charges in the dual formulations of certain low-spin particles and argue that this leads to an infinite number of new conserved charges. [ABSTRACT FROM AUTHOR]

I propose using the group SL (4 , ℝ) as a generalization of the Dirac group SL (2 , ℂ) used in quantum mechanics, in an attempt to match the symmetries of the 'internal' spacetime of elementary particles to the symmetries of the 'external' spacetime of general relativity. While my conclusions do not amount to a new model or theory, they do highlight some specific points where there are apparent conflicts between the mathematics and the physics of the standard model, that might repay closer investigation. As evidence that this mathematical approach may have interesting things to say about physics, I propose two mass equations that seem not to have been observed previously. [ABSTRACT FROM AUTHOR]

Baryons B (Q q q ′) for heavy quarks Q = c , b , t , and light quarks q = u , d , s , are considered. Strong interaction coupling-constant sum rules with first-order breaking of SU(3) flavor symmetry are determined for reactions B → B ′ + M where B = B (Q q q ′) , B ′ = B (Q q q ″) and M = M (q ′ q ̄ ″) is a light meson. Specific applications to couplings of J P = 1 2 + charmed and bottom baryons are presented. Also, SU(3) Clebsch–Gordan coefficients for the product of representations 6 ⊗ 8 are explicitly determined. [ABSTRACT FROM AUTHOR]

Heavy baryons B (Q Q ′ q) and heavy mesons M (Q ̄ q) for heavy quarks Q = c , b , or t and light quarks q = u , d , or s are considered. Strong interaction coupling-constant sum rules with first-order breaking of SU(3) flavor symmetry are obtained for reaction H → H ′ + M (q q ̄ ′) where H = B (Q Q ′ q) or M (Q ̄ q) , H ′ = B (Q Q ′ q ′) or M (Q ̄ q ′) , and M (q q ̄ ′) is a light meson. Specific results for couplings of doubly charmed baryons and charm and bottom mesons are presented. Also, SU(3) Clebsch-Gordan coefficients for the product of representations 3 ⊗ 8 are explicitly determined. [ABSTRACT FROM AUTHOR]

We continue the study undertaken in Ref. 16 of the exceptional Jordan algebra J = J 3 8 as (part of) the finite-dimensional quantum algebra in an almost classical space–time approach to particle physics. Along with reviewing known properties of J and of the associated exceptional Lie groups we argue that the symmetry of the model can be deduced from the Borel–de Siebenthal theory of maximal connected subgroups of simple compact Lie groups. [ABSTRACT FROM AUTHOR]

This paper is a review by the authors concerning the construction of a Poincaré covariant (owing to space-time continuum) field-theoretic formalism in terms of step-function-type basis functions without ultraviolet divergences. This formalism analytically derives confinement/deconfinement, mass-gap and Regge trajectory for non-Abelian gauge fields, and gives solutions for self-interacting scalar fields. Fields propagate in space-time continuum and fields with finite degrees of freedom toward continuum limit have no ultraviolet divergence. Basis functions defined in a parameter space-time are mapped to real space-time. The authors derive a new solution comprised of classical fields as vacuum and quantum fluctuations, leading to the linear potential between the particle and antiparticle from the Wilson loop. The Polyakov line gives finite binding energies and reveals the deconfining property at high temperatures. The quantum action yields positive mass from the classical fields and quantum fluctuations produce the Coulomb potential. Pure Yang-Mills fields show the same mass-gap owing to the particle-antiparticle pair creation. The Dirac equation under linear potential is analytically solved in this formalism, reproducing the principal properties of Regge trajectories at a quantum level. Further outlook mentions a possibility of the difference between conventional continuum and present wave functions responsible for the cosmological constant. [ABSTRACT FROM AUTHOR]

In this paper, we consider a family of systems with two predators feeding on one prey. We show how to construct a positively invariant set in which it is possible to define a Poincaré map for examining the behavior of the system, mainly in the case when both predators survive. We relate it to examples from earlier works. [ABSTRACT FROM AUTHOR]

In the context of the relationship between physics of cosmological dark matter and symmetry of elementary particles, a wide list of dark matter candidates is possible. New symmetries provide stability of different new particles and their combination can lead to a multicomponent dark matter. The pattern of symmetry breaking involves phase transitions in the very early Universe, extending the list of candidates by topological defects and even primordial nonlinear structures. [ABSTRACT FROM AUTHOR]

We discuss a set of novel discrete symmetry transformations of the supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved Noether charges) and two discrete symmetries together provide the physical realizations of the de Rham cohomological operators of differential geometry. We have also exploited the supervariable approach to derive the nilpotent SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions and onto -dimensional supermanifold. [ABSTRACT FROM AUTHOR]

We prove, both for continuous time and discrete time, results establishing convergence to flocking in a model in which each agent is influenced by only a few closest neighbors. We show unconditional convergence to flocking when this number of closest neighbors is at least half of the population and, otherwise, conditional convergence. That is, convergence to flocking provided the initial positions and velocities satisfy an explicit constraint. We also show that the proportion of neighbors necessary for unconditional convergence, one-half, is sharp. Nothing less will do. [ABSTRACT FROM AUTHOR]

We study the possibility of explaining the recently reported 750 GeV di-photon excess at LHC within the framework of a left-right symmetric model. The 750 GeV neutral scalar in the model is dominantly an admixture of neutral components of scalar bidoublets with a tiny fraction of neutral scalar triplet. Incorporating septuplet scalar pairs into the model, we enhance the partial decay width of the 750 GeV neutral scalar into di-photons through charged septuplet components in loop while keeping the neutral septuplet components as subdominant dark matter candidates. The model also predicts the decay width of the 750 GeV scalar to be around 36 GeV to be either confirmed or ruled out by future LHC data. The requirement of producing the correct di-photon signal automatically keeps the septuplet dark matter abundance subdominant in agreement with bounds from direct and indirect detection experiments. We then briefly discuss different possibilities to account for the remaining dark matter component of the Universe in terms of other particle candidates whose stability arises either due to remnant discrete symmetry after spontaneous breaking of or due to high -dimension forbidding their decay into lighter particles. [ABSTRACT FROM AUTHOR]

We discuss the possible violation of local Lorentz invariance (LLI) arising from a faster-than-light neutrino speed. A toy calculation of the LLI violation parameter , based on the (disclaimed) OPERA data, suggests that the values of are determined by the interaction involved, and not by the energy range. This hypothesis is further corroborated by the analysis of the more recent results of the BOREXINO, LVD and ICARUS experiments. [ABSTRACT FROM AUTHOR]