The general-covariant and gauge-invariant theory of quantum particles in classical backgrounds

TL;DR

This paper develops a covariant, gauge-invariant framework for describing quantum particles in classical gravitational and electromagnetic backgrounds, introducing a local particle current operator that accounts for particle production and conservation properties.

Contribution

It introduces a new local, covariant, gauge-invariant operator for particle density in arbitrary backgrounds, linking local particle production to global descriptions via the choice of two-point functions.

Findings

A local particle current operator is constructed for scalar and spinor fields.

Different two-point function choices affect current conservation and particle production descriptions.

The Schwinger-DeWitt method yields a conserved current in the absence of interactions.

Abstract

A new approach to the concept of particles and their production in quantum field theory is developed. A local operator describing the current of particle density is constructed for scalar and spinor fields in arbitrary gravitational and electromagnetic backgrounds. This enables one to describe particles in a local, general-covariant and gauge-invariant way. However, the current depends on the choice of a 2-point function. There is a choice that leads to the local non-conservation of the current in a gravitational or an electromagnetic background, which describes local particle production consistent with the usual global description based on the Bogoliubov transformation. The most natural choice based on the Green function calculated using the Schwinger-DeWitt method leads to the local conservation of the current, provided that interactions with quantum fields are absent. Interactions with quantum fields lead to the local non-conservation of the current which describes local particle production consistent with the usual global description based on the interaction picture.