We discuss the geometry of the Lagrangian quantization scheme based on (generalized) Schwinger-Dyson BRST symmetries. When a certain set of ghost fields are integrated out of the path integral, we recover the Batalin-Vilkovisky formalism, now extended to arbitrary functional measures for the classical fields. Keeping the ghosts reveals the crucial role played by a natural connection on the spac...

We perform the gauge–fixing of the theory of a chiral two–form boson in six dimensions starting from the action given by Pasti, Sorokin and Tonin. We use the Batalin–Vilkovisky formalism, introducing antifields and writing down an extended action satisfying the classical master equation. Then we gauge–fix the three local symmetries of the extended action in two different ways. 1 E-mail: chris.v...

A general method is presented for deriving on-shell Ward-identities in (2D) string theory. It is shown that all tree-level Ward identities can be summarized in a single quadratic differential equation for the generating function of all amplitudes. This result is extended to loop amplitudes and leads to a master equation à la Batalin-Vilkovisky for the complete partition function. supported by t...

The ∆-operator of the Batalin-Vilkovisky formalism is the Hamiltonian BRST charge of Abelian shift transformations in the ghost momentum representation. We generalize this ∆-operator, and its associated hierarchy of antibrackets, to that of an arbitrary non-Abelian and possibly open algebra of any rank. We comment on the possible application of this formalism to closed string field theory. NBI-...

A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology structures. The gravity algebra on the equivariant homology of the free loop space is also modeled. The construction includes the non-simply connected case, and...

A superspace formulation for the Batalin Vilkovisky formalism (also called fieldantifield quantization ) with extended BRST invariance (BRST and anti-BRST invariance ) for gauge theories with closed algebra is presented. In contrast to a recent formulation, where only BRST invariance holds off shell, two collective sets of fields are introduced and an off shell realization of the extended algeb...

Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin (BFT), we embed the second-class non-abelian SU(2) Higgs model in the unitary gauge into a gauge invariant theory. The strongly involutive Hamiltonian and constraints are obtained as an infinite power series in the auxiliary fields. Furthermore, comparing these results with those obtained from the gauge...

The non-local regularization is a powerfull method to regularize theories with an action that can be decomposed in a kinetic and an interacting part. Recently it was shown how to regularize the Batalin-Vilkovisky field-antifield formalism of quantization of gauge theories with the non-local regularization. We compute precisely the anomaly of the Chiral Schwinger model with this extended non-loc...

In the context of the Batalin-Vilkovisky formalism, a new observable for the Abelian BF theory is proposed whose vacuum expectation value is related to the Alexander-Conway polynomial. The three-dimensional case is analyzed explicitly, and it is proved to be anomaly free. Moreover, at the second order in perturbation theory, a new formula for the second coefficient of the Alexander-Conway polyn...

Using the Non-Abelian Batalin-Vilkovisky formalism introduced recently, we present a generalization of the Yang-Mills gauge transformations , to include antisymmetric tensor fields as gauge bosons. The Freedman-Townsend transformation for the two-form gauge field is automatically recovered. New characteristic classes involving this two-form field and the Yang-Mills one-form field are derived. W...