BRST Symmetries for the Tangent Gauge Group

Abstract

For any principal bundle $P$, one can consider the subspace of the space of connections on its tangent bundle $TP$ given by the tangent bundle $T\mathcal{A}$ of the space of connections $\mathcal{A}$ on $P$. The tangent gauge group acts freely on $T\mathcal{A}$. Appropriate BRST operators are introduced for quantum field theories that include as fields elements of $T\mathcal{A}$, as well as tangent vectors to the space of curvatures. As the simplest application, the BRST symmetry of the so-called $BF$-Yang-Mills theory is described and the relevant gauge fixing conditions are analyzed. A brief account on the topological $BF$ theories is also included and the relevant Batalin-Vilkovisky operator is described.

33 pages, TeX; revised version with minor corrections; to appear in J. Math. Phys

References in corpus (2)

• Four-Dimensional Yang-Mills Theory as a Deformation of Topological BF Theory
• Abelian BF Theories and Knot Invariants

Cited by in corpus (1)

• Off-shell BRST-VSUSY superalgebra for D=4 BF theories in the superconnection formalism