Abstract
The origin of the classical BRS symmetry is discussed for the case of a first class constrained system consisting of a 2n-dimensional phase spaceS with free action of a Lie gauge groupG of dimensionm. The extended phase spaceS ext of the Fradkin-Vilkovisky approach is identified with a globally trivial vector bundle overS with fibreL*(G)⊕L(G), whereL(G) is the Lie algebra ofG andL*(G) its dual. It is shown that the structure group of the frame bundle of the supermanifoldS ext is the orthosymplectic group OSp(m,m; 2n), which is the natural invariance group of the super Poisson bracket structure on the function spaceC ∞(S ext). The action of the BRS operator ω is analyzed for the caseS=R 2n with constraints given by pure momenta. The breaking of the osp(m,m; 2n)-invariance down to sp(2n−2m) occurs via an intermediate “osp(m; 2n−m).” Starting from a (2n+2m)-dimensional system with orthosymplectic invariance, different choices for the BRS operator correspond to choosing different 2n-dimensional constraint supermanifolds inS ext, which in general characterize different constrained systems. There is a whole family of physically equivalent BRS operators which can be used to describe a particular constrained system.
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Communicated by A. Jaffe
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Loll, R. The extended phase space of the BRS approach. Commun.Math. Phys. 119, 509–527 (1988). https://doi.org/10.1007/BF01218085
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DOI: https://doi.org/10.1007/BF01218085