BRST detour quantization: Generating gauge theories from constraints

We present the Becchi–Rouet–Stora–Tyutin (BRST) cohomologies of a class of constraint (super) Lie algebras as detour complexes. By interpreting the components of detour complexes as gauge invariances, Bianchi identities, and equations of motion, we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric, and Kahler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form Kahler electromagnetism. We also discuss how our results generalize to other special geometries.