Antifield Formalism Research Articles

COMMENTS ON UNITARITY IN THE ANTIFIELD FORMALISM

The local completeness condition was introduced in the analysis of the locality of the gauge fixed action for gauge systems. This condition expresses that the gauge transformations and the reducibility coefficients should be described in such a way that they contain as few derivatives of the gauge parameters as possible. We show here that this condition not only guarantees that the gauge fixed action is local in space-time (as proved previously), but also that the antifield formalism leads to a unitary theory.

Lectures on the antifield-BRST formalism for gauge theories

The Lagrangian approach to the BRST symmetry based on the antifield formalism is reviewed. First, the concept of “open algebra” is clarified. It is then explicitly indicated how gauge invariance is incorporated in the theory through the BRST cohomology at ghost number zero. This result holds for both the non-gauge fixed and gauge fixed versions of the BRST symmetry in Lagrangian form. The properties of the Lagrangian integration measure are discussed and the role of the Schwinger-Dyson equation is stressed. The problem of spacetime locality of the gauge fixed action is also briefly addressed. The discussion is illustrated in the cases of electromagnetism and of free p-form gauge fields.

Elimination of the auxiliary fields in the antifield formalism

The problem of the elimination of the auxillary fields in the path integral quantization of gauge theories is investigated in the context of the antifield formalism. It is shown that gauge fixing fermions can be found such that: (i) the auxillary fields remain auxiliary after gauge fixing; and (ii) the gauge fixed actions obtained by eliminating the auxillary fields before or after writing down the path integral coincide. The contribution of the auxiliary fields to the integration measure is also discussed. These results are applied (i) to the problem of the equivalence between the lagrangian and hamiltonian path integral formulations; and (ii) to the problem of the elimination of the second class constraints in the hamiltonian formalism.

Antibracket—antifield formalism for constrained hamiltonian systems

Abstract The detailed comparison between the hamiltonian approach to the BRST symmetry and the antibracket—antifield formalism is carried out in the case of first order action principles. This is done by explicitl expressing the solution of the master equation in terms of the hamiltonian BRST charge. Complete agreement is found between both formalisms. This conclusion holds for irreducible and reducible constrained systems. The example of the free relativistic particle is considered.