Algebraic structure of the anti-BRST transformation in Hamiltonian formulation

Despite the fact that the anti-BRST symmetry was formulated for the Yang-Mills theory, it has been generalized for many other theories, being a useful tool in understanding the non-minimal sector, as well as the covariant anomaly. For these reasons, it is of interest to develop an algebraic formalism for the description of the anti-BRST symmetry. This is done in the Hamiltonian formulation by duplicating each first class constraint and by splitting the corresponding Koszul-Tate differential. By introducing a bi-degree we can decompose the BRST charge into two parts: the part of degree (1,0) is the BRST generator in a theory without duplication, and the part of degree (0,1) is the anti-BRST generator. (Author)