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Contents

Idea

In BV-BRST formalism the antibracket is a canonical product operation on an associative algebra generated by fields and antifields. If antifields are regarded as vector fields on the space of fields, then the antibracket is just the (graded) Schouten bracket.

There are different incarnations of the antibracket associated with different incarnations of the algebra of fields/antifields:

Applied to horizontal differential forms on the jet bundle of the field bundle this refines to the local antibracket.

By transgression of variational differential forms this yields the (“global”) antibracket on polynomial observables of a Lagrangian field theory.

For details see at A first idea of quantum field theory the chapter Reduced phase space for the antibracket before quantization, and the chapter Free quantum fields for the (time-ordered) antibracket after quantization.

Related concepts

• BV-operator

References

Review includes

• Marc Henneaux, section 7.3 of Lectures on the Antifield-BRST formalism for gauge theories, Nuclear Physics B (Proceedings Supplement) 18A (1990) 47-106 (pdf)

• Marc Henneaux, Claudio Teitelboim, section 15.5.2 of Quantization of Gauge Systems, Princeton University Press 1992.

• Joaquim Gomis, Jordi Paris, Stuart Samuel, section 4.2 of Antibracket, Antifields and Gauge-Theory Quantization, Phys. Rept. 259 (1995) 1-145 (arXiv:hep-th/9412228)

• Alberto Cattaneo, Carlo Rossi, section 4.2 of Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops, Commun.Math.Phys. 221 (2001) 591-657 (arXiv:0010172)