The vacuum state and minimum energy in Dirac's hole theory

TL;DR

This paper challenges the common assumption in Dirac's hole theory that the vacuum state, with all negative energy states filled, is the lowest energy state, showing that this may not be true.

Contribution

The paper demonstrates that the Dirac sea is not necessarily the minimum energy state, questioning a fundamental aspect of Dirac's hole theory.

Findings

The vacuum state in Dirac's hole theory is not always the minimum energy state.

Theoretical analysis reveals potential for lower energy configurations.

Implications for the validity of Dirac's original assumptions.

Abstract

In Dirac's hole theory the vacuum state is assumed to be the state where all negative energy states are occupied and all positive energy states are unoccupied. This is often referred to as the Dirac sea. It is generally assumed that the Dirac sea is the minimum possible energy state. However it will be shown in this paper that this is not the case.