Solving general gauge theories on inner product spaces

TL;DR

This paper demonstrates a model-independent approach to BRST quantization on inner product spaces, revealing the structure of physical states and their relation to gauge theories, including reducible and irreducible cases.

Contribution

It introduces a generalized quartet mechanism for BRST quantization on inner product spaces, providing a unified framework applicable to various gauge theories and extending previous Lie group solutions.

Findings

Physical states have a specific exponential form involving the BRST operator.

Two types of trivial BRST invariant states are identified, depending on the choice of gauge fixing.

The approach applies to both irreducible and reducible gauge theories within the BFV framework.

Abstract

By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form |ph>=e^{[Q, \psi]} |ph>_0 where Q is the nilpotent BRST operator, \psi a hermitian fermionic gauge fixing operator, and |ph>_0 BRST invariant states determined by a hermitian set of BRST doublets in involution. |ph>_0 does not belong to an inner product space although |ph> does. Since the BRST quartets are split into two sets of hermitian BRST doublets there are two choices for |ph>_0 and the corresponding \psi. When applied to general, both irreducible and reducible, gauge theories of arbitrary rank within the BFV formulation we find that |ph>_0 are trivial BRST invariant states which only depend on the matter variables for one set of solutions, and for the other set |ph>_0 are solutions of a Dirac quantization. This generalizes previous Lie group solutions obtained by means of a bigrading.