Related papers: Chronon corrections to the Dirac equation
We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two…
A toy model for the electroweak interactions(without chirality) is proposed in a six dimensional spacetime with 3 timelike and 3 spacelike coordinates. The spacetime interval $ds^2=dx_\mu dx^\mu$ is left invariant under the symmetry group…
A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equation for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon…
The recent literature shows a renewed interest, with various independent approaches, in the classical theories for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
The distributed system $\mathcal{S}_D$ described by the Dirac equation is investigated simply as a dynamic system, i.e. without usage of quantum principles. The Dirac equation is described in terms of hydrodynamic variables: 4-flux $j^{i}$,…
The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4,R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a…
We demonstrate how a Lorentz covariant formulation of the chiral p-form model in D=2(p+1) containing infinitely many auxiliary fields is related to a Lorentz covariant formulation with only one auxiliary scalar field entering a chiral…
It is shown that a subgroup of $SL(2,{\mathbb H})$, denoted $Spin(2,{\mathbb H})$ in this paper, which is defined by two conditions in addition to unit quaternionic determinant, is locally isomorphic to the restricted Lorentz group,…
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…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
A neo-classical relativistic mechanics theory is presented where the spin of an electron is a natural part of its space-time path as a point particle. The fourth-order equation of motion corresponds to the same Lagrangian function in proper…
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…
This paper presents a relativistic symmetrical interpretation of the Dirac equation in 1+1 dimensions which predicts no zitterbewegung for a free spin-1/2 particle. This could resolve the longstanding puzzle of zitterbewegung in…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
The structure of the Dirac Hamiltonian in 3+1 dimensions is shown to emerge in a semi-classical approximation from a abstract spectral triple construction. The spectral triple is constructed over an algebra of holonomy loops, corresponding…
In the present article, using a further generalization of the algebraic method of separation of variables, the Dirac equation is separated in a family of space-times where it is not possible to find a complete set of first order commuting…