BRST QUANTIZATION OF NON-ABELIAN BF TOPOLOGICAL THEORIES

TL;DR

This paper constructs the BRST charge and invariant action for non-abelian BF topological theories, demonstrating their reducibility, phase space structure, and metric independence of the partition function.

Contribution

It provides an explicit construction of the BRST charge and effective action for non-abelian BF theories, including the extended phase space and reducibility structure.

Findings

Semi-classical approximation fully describes the quantum theory.

Partition function is independent of the metric.

Explicit phase space including ghosts for ghosts is obtained.

Abstract

The off-shell nilpotent BRST charge and the BRST invariant effective action for non-abelian BF topological theories over D-dimensional manifolds are explicitly constructed. These theories have the feature of being reducible with exactly D-3 stages of reducibility. The adequate extended phase space including the different levels of ghosts for ghosts is explicitly obtained. Using the structure of the resulting BRST charge we show that for topological BF theories the semi-classical approximation completely describes the quantum theory. The independence of the partition function on the metric also follows from our explicit construction in a straightforward way.