Erratum: Covariant quantization of gauge theories in the framework of extended BRST symmetry [J. Math. Phys. 3 1, 1487 (1990)]

Linear odd Poisson bracket on Grassmann variables

“…It is a well-known fact that, in contrast with the even Poisson bracket, the nondegenerate odd Poisson bracket has one Grassmann-odd nilpotent differential ∆-operator of the second order, in terms of which the main equation has been formulated in the Batalin-Vilkovisky scheme [5,6,7,8,9,10] for the quantization of gauge theories in the Lagrangian approach. In a formulation of Hamiltonian dynamics by means of the odd Poisson bracket with the help of a Grassmann-odd HamiltonianH (g(H) = 1) [11,12,13,14,15,16,17,18,19,20,21,22] this ∆-operator plays also a very important role being used to distinguish the non-dissipative dynamical systems, for which ∆H = 0, from the dissipative ones [1], for which the Grassmann-odd Hamiltonian satisfies the condition ∆H = 0.…”

Gauge fixing in the Lagrangian formalism of superfield BRST quantization

“…Furthermore, as in the theorems proved by the study of [10], one can establish the fact that any solution δX of Eq. (21), vanishing when all the variables entering δX are equal to zero, has the form (25), with a certain fermionic functional δΨ.…”

Space-time locality in theSp(2)-symmetric Lagrangian formalism

“…Two functionals S and S ′ are called gauge equivalent if they are related by (13). In [3] it is shown that G transformations do not change the physical contents of the theory. Let us proceed by studying the general solution to the Sp(2) master equation in first order on C αa , B α .…”

“…5 In [3], it was postulated thatΛ ij α = 0. In fact, we see, thatΛ ij α can be removed by a G transformation.…”

“…Ghost and antighost variables, BRST and anti-BRST charges and the pair of equations for the effective action form Sp(2) doublets. In [2]- [7], the formal proof of the existence of a solution to the Sp(2) master equation and description of the arbitrariness of solutions were given. In those papers, however, the locality of the effective action was assumed as a hypothesis.…”