The most general combination of couplings of fermions with external potentials in 1+1 dimensions, must include vector, scalar and pseudoscalar potentials. We consider such a mixing of potentials in a PT-symmetric time-independent Dirac equation. The Dirac equation is mapped into an effective PT-symmetric Schrödinger equation. Despite the non-hermiticity of the effective potential, we find real ...

We study (1 + 1) dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo supersymmetry.

A derivation of the Dirac equation in ‘3 + 1’ dimensions is presented based on a master equation approach originally developed for the ‘1+ 1’ problem by McKeon and Ord. The method of derivation presented here suggests a mechanism by which the work of Knuth and Bahrenyi on causal sets may be extended to a derivation of the Dirac equation in the context of an inference problem.

The relation between the two most important in mathematical physics first order systems of partial differential equations is among those topics which attract attention because of their general, even philosophical significance but at the same time do not offer much for the solution of particular problems concerning physical models. The Maxwell equations can be represented in a Dirac like form in...

Dirac equation for the finite dipole potential is solved by the method of the join of the asymptotics. The formulas for the near continuum state energy term of a relativistic electron-dipole system are obtained analytically. Two cases are considered: Z < 137 and Z > 137 Dirac equation for Z > 137 is solved by usual method of cut-off potential at small distances.

The Dirac equation, usually obtained by 'quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic continuation, making the model 'self-quantizing'. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum...

We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic example of the non-relativistic harmonic oscillator with radiation reaction. We also illustrate removal of the noncasual pre-acceleration with the introductio...

It is shown that the Dirac sea can be uniquely defined for the Dirac equation with general interaction, if we impose a causality condition on the Dirac sea. We derive an explicit formula for the Dirac sea in terms of a power series in the bosonic potentials. The construction is extended to systems of Dirac seas. If the system contains chiral fermions, the causality condition yields a restrictio...

Classical model Sdc of Dirac particle SD is constructed. SD is the dynamic system described by the Dirac equation. Its classical analog Sdc is described by a system of ordinary differential equations, containing the quantum constant h̄ as a parameter. Dynamic equations for Sdc are determined by the Dirac equation uniquely. Both dynamic systems SD and Sdc appear to be nonrelativistic. One succeed...

A new algebraic technique for solving Schrödinger and Klein-Gordon equations [1], and the related other works therein, has been introduced recently and used to search many interesting problems in different disciplines of physics. These works have clarified the power of the suggested model when compared the results obtained with those provided by other analytical methods in the literature. Never...