Global Symmetries in the Antifield-Formalism

TL;DR

This paper demonstrates how global symmetries can be extended within the antifield formalism and identifies obstructions to incorporating these symmetries when higher order conservation laws are present.

Contribution

It shows that global symmetries can be extended to ghosts and antifields in the antifield formalism and reveals obstructions caused by higher order conservation laws.

Findings

Global symmetries can be extended to ghosts and antifields.

Obstructions exist in incorporating rigid symmetries due to higher order conservation laws.

Explicit examples illustrate the obstructions.

Abstract

In this paper, two things are done. (i) First, it is shown that any global symmetry of a gauge-invariant theory can be extended to the ghosts and the antifields so as to leave invariant the solution of the master-equation (before gauge fixing). (ii) Second, it is proved that the incorporation of the rigid symmetries to the solution of the master-equation through the introduction of a constant ghost for each global symmetry can be obstructed already at the classical level whenever the theory possesses higher order conservation laws. Explicit examples are given.