A fermionic analogue of the Groenwald-van Hove theorem and the Hamiltonian BRST charge

Abstract

A fermionic analogue of the Groenwald-van Hove theorem is studied within the Kostant-Sternberg framework for the BRST ghosts. In gauge theories with semi-simple Lie groups, the BRST generator evades the fermionic version of Groenwald-van Hove theorem and inherits the nilpotency of the classical BRST charge mainly because of the particular structure of the classical charge, although the homomorphic property between the super-commutator and the super-Poisson bracket is problematical from the viewpoint of the theorem in quantization of cubic polynomials like the BRST charge. Avoiding the theorem is possibly one of the restrictions on the BRST charge in its construction in general constrained systems with the BRST generator involving ghost powers of order higher than three.