BRST-anti-BRST covariant theory for the second class constrained systems: A general method and examples Original Research Article

An BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for 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. The formalism displays explicitly the Sp(2) × Sp(2) symmetry property. Surprisingly, the BRST-anti-BRST algebra must involve a central element, related to the non-vanishing part of the constraint commutator and has 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 compared to a first class theory or split involution second class case in the non-symmetric formulation. The general method of construction is supplemented by the explicit derivation of the extended BRST symmetry generators for several examples of second class theories, including the self-dual non-abelian model and massive Yang-Mills theory.