Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-08-14
Phys.Lett. B417 (1998) 259-268
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX 2.09, 13pp
Scientific paper
10.1016/S0370-2693(97)01404-4
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.
Grigoriev M. A.
~Semikhatov ~M. A.
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