Gauge fixing, co-BRST and time evolution in QED

TL;DR

This paper explores the construction of BRST-invariant states in quantum electrodynamics, analyzing gauge fixing, co-BRST operators, and their relation to time evolution of states.

Contribution

It introduces a method to construct BRST-invariant states using trivial states and gauge regulators, and examines their evolution and gauge fixing relations.

Findings

Identified co-BRST operators and gauge-fixing regulators.

Established the relation between gauge fixing and time evolution.

Constructed BRST-invariant inner product states.

Abstract

We consider BRST-invariant inner product states for quantum electrodynamics constructed from trivial BRST-invariant states and a gauge regulator. The trivial states are products of matter and ghost states and are annihilated by hermitian operators. The co-BRST operator and some further gauge-fixing regulators are found. The relation between gauge fixing and time evolution of both the trivial and the inner product states is discussed.