Physics

Chiral symmetry is included into the Dirac equation using the irreducible representations of the Poincaré group. The symmetry introduces the chiral angle that specifies the chiral basis. It is shown that the correct identification of these basis allows explaining small masses of neutrinos and predicting a new candidate for Dark Matter massive particle.

The solution of the Liouville equation for the ensemble of free particles is presented and the classical analog to the quantum accelerating Airy wave packet is constructed and discussed. Considering the motion of various classical packets -- with an infinite and restricted distribution of velocities of particles -- and also the motion of their fronts, we demonstrate in the simplest and most definite way why the packet can display a more sophisticated behavior (even acceleration) as compared with a free individual particle that moves at a fixed velocity. A comparison of this classical solution with the quantum one in the Wigner representation of quantum mechanics which provides the closest analogy is also presented.

This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigory Perelman's entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entropy, mutual information etc. We formulate the concept of the entanglement entropy of quantum geometric information flows and study properties and inequalities for quantum, thermodynamic and geometric entropies characterising such systems.

We have extended our result on defocussing of world lines [1] by modifying gravity in the early epoch by a 5-d theory with scalar ψ(r) . The acceleration term in the Raychaudhuri equation has been shown to be positive for flat FRW metric. The scalar ψ(r) satisfies a non-linear differential equation which is solved. Though singular, the acceleration term turns out to be finite. With this, the equations for the Hubble parameter H(t) and the scale factor a(t) are obtained. These are analyzed using 'fixed point analysis'. Without the scalar field, the age of the universe is finite showing a beginning of the universe and with out bounce. With the contribution of the scalar included, the age of the universe is shown to be infinite, thereby resolving the singularity. The scale factor a(t) exhibits classical bounce, the bounce being proportional to the effect of the scalar field. The effect of the 5-d gravity in the early universe is to cause defocussing of the world lines, give infinite age of the universe thereby resolving the big bang singularity and classical bounce for the FRW scale factor.

This article develops the algebraic structure that results from the θ -commutator αβ− e iθ βα=1 that provides a continuous interpolation between the Clifford and Heisenberg algebras. We first demonstrate the most general geometrical picture, applicable to all values of N . After listing the properties of this Hilbert space, we study the generalized coherent states that result when ξ N =0 , for N≥2 . We also solve the generalized harmonic oscillator problem and derive generalized versions of the Hermite polynomials for general N . Some remarks are made to connect this study to the case of anyons. This study represents the first steps towards developing an anyonic field theory.

Without the mass-energy equivalence available on Minkowski spacetime M , it is not possible on 4-dimensional non-relativistic Galilei/Newton spacetime G to combine 3-momentum and total mass-energy in a single tensor object. However, given a fiducial frame, it is possible to combine 3-momentum and kinetic energy into a linear form (particle) or (1,1) tensor (continuum) in a manner that exhibits increased unity of classical mechanics on flat relativistic and non-relativistic spacetimes M and G . As on M , for a material continuum on G the First Law of Thermodynamics can be considered a consequence of a unified dynamical law for energy-momentum rather than an independent postulate.

We analyze the attempt by C. Corda to explain the results of modern Moessbauer experiments in a rotating system via the additional effect of synchronization of the clock in the origin of the rotating system with the laboratory clock, and indicate errors committed by him.

A rebuttal of a recent article by Hirsch J.E. is presented below. To begin with, the main assumption, regarding the Meissner effect, which the whole argument relies upon, is disproved. Besides, the subsequent analysis misconstrues an original view of the Meissner effect by other authors [2]. Finally, the discussion of the Joule effect turns out to violate the first law of thermodynamics.

Few comments upon Gonzalez-Fernandez and Camacho paper (arXiv: 1904.02299) are pointed out. We bring evidences that the analogue gravity recipe does not work for a BEC in an anisotropic harmonic-oscillator trap. The analogy with an accelerated observer does not seem to be realistic. Some loopholes related to the physical units are emphasized.

In the paper by P. Quincey (2020) [1], the author claims that angles are not dimensionless quantities and that the radian should be a new independent base unit. However, the claim is not supported and the proposed redefinition will cause several problems not only in physics, but also in mathematics. The proposed "unhiding" of the radian will bring hidden problems not discussed in detail. This includes e.g. an introduction of quantities of different kind for time and the corresponding units defined as the second per radian.