Reducible Quantum Electrodynamics. II. The charged states of the vacuum

TL;DR

This paper constructs explicit free Dirac field operators and their expectation values, demonstrating their mathematical well-definedness and providing a foundation for understanding charged states in reducible quantum electrodynamics.

Contribution

It offers an explicit construction of free Dirac field operators and their expectation values within reducible quantum electrodynamics, ensuring mathematical rigor.

Findings

Explicit free Dirac field operators satisfying the Dirac equation

Expectation values form spinors satisfying the Dirac equation

Current operators expressed as pair correlation functions

Abstract

An explicit construction is given of field operators satisfying the free Dirac equation. The quantum expectation of these field operators forms a spinor which satisfies the original Dirac equation. The current operators are defined as pair correlation functions. Explicit expressions in terms of creation and annihilation operators are obtained. A small example shows that all relevant quantities are mathematically well-defined.