Simple BRST quantization of general gauge models

It is shown that the BRST charge $Q$ for any gauge model with a Lie algebra symmetry may be decomposed as Q=\del+\del^{\dag}, \del^2=\del^{\dag 2}=0, [\del, \del^{\dag}]_+=0 provided dynamical Lagrange multipliers are used but without introducing other matter variables in \del than the gauge generators in $Q$. Furthermore, \del is shown to have the form \del=c^{\dag a}\phi_a (or $\phi'_ac^{\dag a}$) where $c^a$ are anticommuting expressions in the ghosts and Lagrange multipliers, and where the non-hermitian operators $\phi_a$ satisfy the same Lie algebra as the original gauge generators. By means of a bigrading the BRST condition reduces to \del|ph\hb=\del^{\dag}|ph\hb=0 which is naturally solved by c^a|ph\hb=\phi_a|ph\hb=0 (or c^{\dag a}|ph\hb={\phi'_a}^{\dag}|ph\hb=0). The general solutions are shown to have a very simple form.Comment: 18 pages, Late

A note on path integrals and time evolutions in BRST quantization

Recent formal solutions of BRST quantization on inner product spaces within the operator method are shown to lead to an unexpected interpretation of the conventional path integral formulation. The relation between the Hamiltonians in the two formulations is nontrivial. For the operator method the correspondence requires certain quantum rules which make the formal solutions exact, and for the path integral the correspondence yields a precise connection between boundary conditions and the choice of gauge fixing.Comment: 11,ITP-G\"{o}teborg 93-19, latexfil

Proper BRST quantization of relativistic particles

Recently derived general formal solutions of a BRST quantization on inner product spaces of irreducible Lie group gauge theories are applied to trivial models and relativistic particle models for particles with spin 0, 1/2 and 1. In the process general quantization rules are discovered which make the formal solutions exact. The treatment also give evidence that the formal solutions are directly generalizable to theories with graded gauge symmetries. For relativistic particles reasonable results are obtained although there exists no completely Lorentz covariant quantization of the coordinate and momenta on inner product spaces. There are two inequivalent procedures depending on whether or not the time coordinate is quantized with positive or indefinite metric states. The latter is connected to propagators.Comment: 37,ITP-G\"{o}teborg 93-18, latexfil

Quantum antibrackets

A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket as commutators to Poisson brackets. It is explained how this quantum antibracket is related to the classical antibracket and the \Delta-operator in the BV-quantization. Higher quantum antibrackets are introduced in terms of generating operators, which automatically yield all their subsequent Jacobi identities as well as the consistent Leibniz' rules.Comment: 12 pages,Latexfile,Corrected misprint in (43

Time evolution in general gauge theories defined on inner product spaces

As previously shown BRST singlets |s> in a BRST quantization of general gauge theories on inner product spaces may be represented in the form |s>=e^{[Q, \psi]} |\phi> where |\phi> is either a trivially BRST invariant state which only depends on the matter variables, or a solution of a Dirac quantization. \psi is a corresponding fermionic gauge fixing operator. In this paper it is shown that the time evolution is determined by the singlet states of the corresponding reparametrization invariant theory. The general case when the constraints and Hamiltonians may have explicit time dependence is treated.Comment: 12 pages,latexfil