nLab
antibracket

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

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.

The global antibracket is closely related to the BV-operator. See there fore more.

References

Review includes

Last revised on January 9, 2018 at 13:10:16. See the history of this page for a list of all contributions to it.