Related papers: The Dirac Equation Revisited
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory…
This paper can be seen as an exercise in how to adapt quantum mechanics from a strict relativistic perspective while being respectful and critical towards the experimental achievements of the contemporary theory. The result is a fully…
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…
In order to avoid the difficulties encountered by relativistic quantum theory of single particles, we pursue a deductive development of the theory from physical principles, without canonical quantization, by making use of group-theoretical…
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…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
Einstein's Special Theory of Relativity was proposed a little over a hundred years back. It remained a bedrock of twentieth century physics right up to Quantum Field Theory. However, the failure over several decades to provide a unified…
This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory.…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
A concise discussion of the 3-dimensional irreducible (1,0) and (0,1) representations of the restricted Lorentz group and their application to the description of the electromagnetic field is given. It is shown that a mass term is in…
We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group.Lorentz coordinate transformations are derived in a novel…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
The derivation becomes possible when we find a new formalism which connects the relativistic mechanics with the quantum mechanics. In this paper, we explore the quantum wave nature from the Newtonian mechanics by using a concept: velocity…
The work is devoted to the generalization of the Dirac equation for a flat locally anisotropic, i.e., Finslerian space-time. At first we reproduce the corresponding metric and a group of the generalized Lorentz transformations, which has…
The present work is a brief review of the recent development in the relativistic quantum mechanics in the $(1/2)\oplus (0,1/2)$ representation space. It can be useful for graduate students in particle physics and quantum field theory.
A variation of Dirac equation based on SO(2,1) group is suggested for treating low dimensional systems in the three dimensional x,y,t space. Non-unitary representations are developed in an analogous way to those used in the ordinary Dirac…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds…
Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of quantum objects nature has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could…