The BRST quantization of second-class constrained systems Original Research Article

The problem of quantization of second-class constrained systems where the constraint functions, denoted by χα = (Ga, Ca), are such that the Gaʹs are first class among themselves, is considered in the context of the BRST formalism based on path integrals. In this paper is shown that (i) there exists a first-class constrained system classically equivalent to the original second-class one; (ii) there is a gauge fermion implementing the canonical gauge conditions, Ca = 0, such that the BRST quantization of the first-class constrained system is equivalent with the quantization of the original second-class constrained one; (iii) the local measure in the path integral contains k-th order derivatives of the canonical Hamiltonian associated to the original system with respect to the functions Ca(k ⩾ 2). It is also derived the Lagrangian form of the path integral corresponding to the second-class constrained system under discussion in the special case of the original Hamiltonian being at most quadratic in the functions Ca. These results are exemplified on three representative models.