BRST Symmetries for the Tangent Gauge Group

Details BRST Symmetries for the Tangent Gauge Group BRST Symmetries for the Tangent Gauge Group

1997-06-23

arxiv.org/abs/hep-th/9706160v2

J.Math.Phys. 39 (1998) 1316-1339

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1063/1.532381

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 $T{\cal A}$ of the space of connections ${\cal A}$ on $P$. The tangent gauge group acts freely on $T{\cal A}$. Appropriate BRST operators are introduced for quantum field theories that include as fields elements of $T{\cal A}$, 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.

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