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On the Canonical Form of a Pair of Compatible Antibrackets | | M A Grigoriev
; A M Semikhatov
; | | Date: |
14 Aug 1997 | | Journal: | Phys.Lett. B417 (1998) 259-268 | | Subject: | hep-th | | Affiliation: | Lebedev Physics Institute | | 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. | | Source: | arXiv, hep-th/9708077 | | Services: | Forum | Review | PDF | Favorites | |
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