The Batalin-Vilkovisky method (BV ) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangi...

In this paper we extend a theorem of Nicolaescu on spectral flow and the Maslov index. We do this by studying the manifold of Lagrangian subspaces of a symplectic Hilbert space that are Fredholm with respect to a given Lagrangian L0. In particular, we consider the neighborhoods in this manifold of Lagrangians which intersect L0 nontrivially.

Gravitational analogues of the nonlinear electrodynamics of Born and of Born and Infeld are introduced and applied to the black hole problem. This work is mainly devoted to the 2-dimensional case in which the relevant lagrangians are nonpolynomial in the scalar curvature.

A nonlinearly realized supersymmetric action describing the invariant couplings of the Goldstino to matter is constructed. Using the Akulov-Volkov Lagrangian, any operator can be made part of a supersymmetric invariant action. Of particular interest are interaction terms which include the product of the Akulov-Volkov Lagrangian with the ordinary matter Lagrangian as well as the coupling of the ...

We investigate the existence of Intrinsic Localized Modes (ILMs) in nonlinear one-dimensional KleinGordon chains. We use the Lagrangian averaging approach parameterizing ILM by several slow-varying variables, and apply the averaging directly in the action principle. Our preliminary studies yield results for ILM dynamics in accordance with those obtained by other methods.