We propose an algorithm for the construction of higher order gauge field theories from a superfield formulation within the Batalin-Vilkovisky formalism. This is a generalization of the superfield algorithm recently considered by Batalin and Marnelius. This generalization seems to allow for non-topological gauge field theories as well as alternative representations of topological ones. A five di...

A very general and powerful approach to quantization of gauge theories was proposed by Batalin and Vilkovisky [1],[2]. The present paper is devoted to the study of geometry of this quantization procedure. The main mathematical objects under consideration are P -manifolds and SP -manifolds (supermanifolds provided with an odd symplectic structure and, in the case of SP -manifolds, with a volume ...

We show that the reduced Hochschild homology of a DG open Frobenius algebra has the natural structure of a Batalin-Vilkovisky coalgebra, and the reduced cyclic homology has the natural structure of a gravity coalgebra. This gives an algebraic model for a Batalin-Vilkovisky coalgebra structure on the reduced homology of the free loop space of a simply connected closed oriented manifold, and a gr...

2 Path Integrals 3 2.1 Gaussian Integrals and Beyond... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Gauge-fixing Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Gauge-fixing: Faddeev—Popov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Gauge-fixing: BRST . . . . . . . . . . . . . . . . . . . . . . ...

We present a quantization of previously proposed generalized Chern-Simons theory with gl(1,R) algebra in 1+1 dimensions. This simplest model shares the common features of generalized CS theories: on-shell reducibility and violations of regularity. On-shell reducibility of the theory requires us to use the Lagrangian Batalin-Vilkovisky and/or Hamiltonian Batalin-Fradkin-Vilkovisky formulation. S...

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak...

We review and extend the Alexandrov–Kontsevich– Schwarz–Zaboronsky construction of solutions of the Batalin–Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin–Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, t...

We perform the Batalin-Vilkovisky analysis of gauge-fixing for graded Chern-Simons theories. Upon constructing an appropriate gauge-fixing fermion, we implement a Landau-type constraint, finding a simple form of the gauge-fixed action. This allows us to extract the associated Feynman rules taking into account the role of ghosts and antighosts. Our gauge-fixing procedure allows for zero-modes, h...