Central extensions, classical non-equivariant maps and residual symmetries

TL;DR

This paper explores the role of central extensions and residual symmetries in classical theories, linking classical anomalies with non-equivariant maps and introducing a model-independent notion of residual symmetry in electromagnetic backgrounds.

Contribution

It introduces the concept of residual symmetry in non-vanishing EM backgrounds and connects classical anomalies with non-equivariant maps, providing a Lie-algebraic, model-independent framework.

Findings

Classical anomalies are associated with non-equivariant maps.

Residual symmetry is a Lie-algebraic, model-independent concept.

The paper clarifies the role of central extensions in classical contexts.

Abstract

The arising of central extensions is discussed in two contexts. At first classical counterparts of quantum anomalies (deserving being named as "classical anomalies") are associated with a peculiar subclass of the non-equivariant maps. Further, the notion of "residual symmetry" for theories formulated in given non-vanishing EM backgrounds is introduced. It is pointed out that this is a Lie-algebraic, model-independent, concept.