Solving general gauge theories on inner product spaces

Details Solving general gauge theories on inner product spaces Solving general gauge theories on inner product spaces

1995-01-03

arxiv.org/abs/hep-th/9501004v1

Nucl.Phys. B442 (1995) 669-696

Physics

High Energy Physics

High Energy Physics - Theory

25 pages,latexfile

Scientific paper

10.1016/0550-3213(95)00141-E

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.

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