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On the Canonical Form of a Pair of Compatible Antibrackets

M A Grigoriev·A M Semikhatov
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Abstract

In the triplectic quantization of general gauge theories, we prove a `triplectic' analogue of the Darboux theorem: we show that the doublet of compatible antibrackets can be brought to a weakly-canonical form provided the general triplectic axioms of [BMS] are imposed together with some additional requirements that can be formulated in terms of marked functions of the antibrackets. The weakly-canonical antibrackets involve an obstruction to bringing them to the canonical form. We also classify the `triplectic' odd vectors fields compatible with the weakly-canonical antibrackets and construct the Poisson bracket associated with the antibrackets and the odd vector fields. We formulate the Sp(2)-covariance requirement for the antibrackets and the vector fields; whenever the obstruction to the canonical form of the antibrackets vanishes, the Sp(2)-covariance condition implies the canonical form of the triplectic vector fields.

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M A Grigoriev, A M Semikhatov. 1997-08-14. On the Canonical Form of a Pair of Compatible Antibrackets. https://doi.org/10.1016/s0370-2693(97)01404-4

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