BRST-anti-BRST covariant theory for the second class constrained systems. A general method and examples

TL;DR

This paper develops a covariant BRST-anti-BRST formalism for second class constrained systems, revealing new algebraic structures and providing explicit examples including nonabelian models and massive Yang-Mills theory.

Contribution

It introduces a general method for covariant quantization of second class systems using BRST-anti-BRST symmetry, highlighting the role of a central element in the algebra.

Findings

Formalism exhibits explicit Sp(2)×Sp(2) symmetry.

Central element in the algebra relates to nonvanishing constraint commutator.

Explicit generators derived for specific models like nonabelian and massive Yang-Mills.

Abstract

The BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for the second class constrained theories. The constraint algebra generating equations involve on equal footing a pair of BRST charges for second class constraints and a pair of the respective anti-BRST charges. Formalism displays explicit Sp(2) \times Sp(2) symmetry property. Surprisingly, the the BRST-anti-BRST algebra must involve a central element, related to the nonvanishing part of the constraint commutator and having no direct analogue in a first class theory. The unitarizing Hamiltonian is fixed by the requirement of the explicit BRST-anti-BRST symmetry with a much more restricted ambiguity if compare to a first class theory or split involution second class case in the nonsymmetric formulation. The general method construction is supplemented by the explicit derivation of the extended BRST symmetry generators for several examples of the second class theories, including self--dual nonabelian model and massive Yang Mills theory.