The difference between Dirac's hole theory and quantum field theory

TL;DR

This paper investigates the differences between Dirac's hole theory and quantum field theory, highlighting how their results diverge in certain problems and exploring the implications for quantum calculations.

Contribution

It demonstrates that despite their perceived equivalence, Dirac's hole theory and quantum field theory produce different results in specific cases, challenging assumptions of their equivalence.

Findings

Field theory can be derived from hole theory via second quantization

Problems yield different results in the two theories

Differences impact calculation methods in quantum theory

Abstract

Dirac's hole theory and quantum field theory are generally thought to be equivalent. In fact field theory can be derived from hole theory through the process of second quantization. However, it can be shown that problems worked in both theories yield different results. The reason for the difference between the two theories will be examined and the effect the this difference has on the way calculations are done in quantum theory will be examined.