Relativistically Covariant Symmetry in QED

TL;DR

This paper develops a generalized relativistically covariant symmetry in quantum electrodynamics (QED), extending previous symmetries, and explores its properties, including the associated Noether charge and implications for physical states.

Contribution

It introduces a new, more general covariant symmetry in QED, unifying previous symmetries and analyzing its algebraic and physical implications.

Findings

Constructed a covariant symmetry encompassing previous ones.

Derived the Noether charge and its role in physical state constraints.

Showed how auxiliary fields can ensure nilpotency of the symmetry.

Abstract

We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain condition. The Noether charge generating the symmetry transformation is obtained, and it imposes a constraint on the physical states.