Related papers: Dirac Representation of Dynamically-Generated Elem…
We define a new dynamical variable, the relative existence e, in terms of space and time. Taking it as a generalized positional coordinate, we show that for conservative systems the canonically conjugated momentum is identified as the…
The construction of discrete scalar wave propagation equations in arbitrary inhomogeneous media was recently achieved by using elementary dynamical processes realizing a discrete counterpart of the Huygens principle. In this paper, we…
We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the…
Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current…
The unitary irreducible representations of the covering group of the Poincare group P define the framework for much of particle physics on the physical Minkowski space P/L, where L is the Lorentz group. While extraordinarily successful, it…
It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac…
A novel theory of the structure of elementary particles is outlined. The proposed relativistic covariant space-time approach supposes that all massive particles are composite particles formed by massless elementary particles with opposite…
We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein--Gordon equation with a universal length scale. Starting from a singularly perturbed variant of Maxwell's equations, we deduce a 32-dimensional…
It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac…
The space-time symmetry group of a model of a relativistic spin 1/2 elementary particle, which satisfies Dirac's equation when quantized, is analyzed. It is shown that this group, larger than the Poincare group, also contains space-time…
Postulating that spacetime is discrete, we assume that physical space is described by a 3-dimensional cubic lattice.The corresponding symmetry group of rotations has order 24 and motivates the introduction of a cubic shaped graph with 27…
We present a new quantum algebraic description of an electron localized in space-time. Positions in space and time, mass and Clifford generators are defined as quantum operators. Commutation relations and relativistic shifts under frame…
The quantum mechanical description of phase remains a fundamental challenge, with theoretical efforts tracing from the early works of London and Dirac to discrete formalisms. In this work, we extend the action-angle formalism to the…
Recently, a Dirac exceptional point (EP) was reported in a non-Hermitian system. Unlike a Dirac point in Hermitian systems, this Dirac EP has coalesced eigenstates in addition to the degenerate energy. Also different from a typical EP, the…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincar\'e generators explicitly from field operators and show that in the vector spaces for the…
The paper considers a slightly modified one-dimensional infinite mass-in-mass chain. In the case of the long-wave approximation, which corresponds to the transition to a continuous medium, we obtained a system of two equations, which is a…
The class of the free relativistic covariant equations generated by the fractional powers of the D'Alambertian operator $(\square^{1/n})$ is studied. Meanwhile the equations corresponding to n=1 and 2 (Klein-Gordon and Dirac equations) are…
An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a…
We show that the mass of a self-interacting dark matter candidate, specifically a Dirac fermion, can be generated by composite dynamics, with a light scalar mediator emerging alongside the Higgs itself as composite particles. These novel…