Residual Symmetries in the Presence of an EM Background

TL;DR

This paper investigates the residual symmetry algebra of quantum field theories in external electromagnetic backgrounds, extending previous results and explicitly computing the algebra for constant backgrounds in three and four dimensions.

Contribution

It provides a Lie-algebraic, model-independent analysis of residual symmetries, including explicit calculations for constant EM backgrounds in D=3 and D=4.

Findings

In D=3, the residual symmetry algebra is isomorphic to u(1) plus a centrally extended 2D Poincaré algebra.

In D=4, the residual symmetry algebra is a seven-dimensional solvable Lie algebra.

Residual symmetries are also computed for specific non-constant EM backgrounds.

Abstract

The symmetry algebra of a QFT in the presence of an external EM background (named "residual symmetry") is investigated within a Lie-algebraic, model independent scheme. Some results previously encountered in the literature are here extended. In particular we compute the symmetry algebra for a constant EM background in D=3 and D=4 dimensions. In D= 3 dimensions the residual symmetry algebra is isomorphic to $u(1)\oplus {\cal P}_c(2)$, with ${\cal P}_c(2)$ the centrally extended 2-dimensional Poincar\'e algebra. In D=4 dimension the generic residual symmetry algebra is given by a seven-dimensional solvable Lie algebra which is explicitly computed. Residual symmetry algebras are also computed for specific non-constant EM backgrounds.