Dirac theory from a field theoretic point of view

TL;DR

This paper develops a field theoretic framework for the Dirac theory, clarifying the distinction between one-particle and many-particle effects and introducing novel methods for handling Dirac and quantum field theories.

Contribution

It introduces a new field theoretic approach to Dirac theory by embedding Grassmann algebra into Clifford algebra, offering fresh insights and methods for quantum field theory.

Findings

A novel functional equation with unusual behavior

New methods for Dirac and quantum field theory analysis

Clarification of one-particle versus many-particle effects

Abstract

Several complications arise in quantum field theory because of the infinite many degrees of freedom. However, the distinction between one-particle and many-particle effects -- mainly induced by the vacuum -- is not clear up to now. A field theoretic picture of the one-particle Dirac theory is developed in order to explore such questions. Main emphasis is laid on the injection of Grassmann's algebra into the endomorphism Clifford algebra built over it. The obtained ``field theoretic'' functional equation behaves in a very unusual way. New methods to handle Dirac and QFT are given.