The Particle-Field Theory and Its Relativistic Generalization

TL;DR

This paper develops a relativistic extension of the particle-field theory, deriving Lorentz-invariant equations of motion and a relativistic Schrödinger equation, and applies it to a micro-particle in a box to analyze its energy spectrum.

Contribution

It introduces a Lorentz-invariant relativistic generalization of the particle-field theory and derives a new relativistic Schrödinger equation for micro-entities.

Findings

Derived Lorentz-invariant equations of motion for PF systems

Formulated a relativistic Schrödinger equation for micro-particles

Solved the equation for a particle in a one-dimensional box

Abstract

As a serious attempt for constructing a new foundation for describing micro-entities from a causal standpoint, it was explained before in [1, 2, 3] that by unifying the concepts of information, matter and energy, each micro-entity is assumed to be composed of a probability field joined to a particle called a particle-field or PF system. In this essay, the relativistic generalization of the PF theory has been considered. The equation of motion for the PF system is derived in a form which is Lorentz-invariant. Moreover, based on constitutional similarities to classical equations of motion, a well-defined relativistic time-independent Schrodinger equation is derived, which is one of our main achievements in developing a micro-relativistic physics of PF theory. This relativistic Schrodinger equation is solved for a relativistic micro-particle in one-dimensional box to find its eigenstate and energy spectrum.