BRST quantization of topological field theory

The canonical quantization of the topological field-theory model ∫MF∧B, proposed by Horowitz, is examined through the Becchi-Rouet-Stora-Tyutin approach. With this approach we have a manifestly covariant description of a certain class of topological quantum field theories. However, if M in the present model is any orientable four-dimensional manifold, one would end up with different theories when different polarizations are chosen. Therefore a restriction M=R¹×Σ, as pointed out by Horowitz, is required for consistency.