On a path integral with a topological constraint

We discuss a new method to evaluate a path integral with a topological constraint involving a point singularity in a plane. The path integration is performed explicitly in the universal covering space. Our method is an alternative to an earlier method of Inomata

Koopman-von Neumann Formulation of Classical Yang-Mills Theories: I

In this paper we present the Koopman-von Neumann (KvN) formulation of classical non-Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang-Mills theories concepts like gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang-Mills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications.Comment: 46 pages, Late

Universal Hidden Supersymmetry in Classical Mechanics and its Local Extension

We review here a path-integral approach to classical mechanics and explore the geometrical meaning of this construction. In particular we bring to light a universal hidden BRS invariance and its geometrical relevance for the Cartan calculus on symplectic manifolds. Together with this BRS invariance we also show the presence of a universal hidden genuine non-relativistic supersymmetry. In an attempt to understand its geometry we make this susy local following the analogous construction done for the supersymmetric quantum mechanics of Witten.Comment: 6 pages, latex, Volkov Memorial Proceeding

Entanglement Entropy for Relevant and Geometric Perturbations

We continue the study of entanglement entropy for a QFT through a perturbative expansion of the path integral definition of the reduced density matrix. The universal entanglement entropy for a CFT perturbed by a relevant operator is calculated to second order in the coupling. We also explore the geometric dependence of entanglement entropy for a deformed planar entangling surface, finding surprises at second order.Comment: 18 pages + appendice

Thermodynamic behavior of IIA string theory on a pp-wave

We obtain the thermal one loop free energy and the Hagedorn temperature of IIA superstring theory on the pp-wave geometry which comes from the circle compactification of the maximally supersymmetric eleven dimensional one. We use both operator and path integral methods and find the complete agreement between them in the free energy expression. In particular, the free energy in the $\mu \to \infty$ limit is shown to be identical with that of IIB string theory on maximally supersymmetric pp-wave, which indicates the universal thermal behavior of strings in the large class of pp-wave backgrounds. We show that the zero point energy and the modular properties of the free energy are naturally incorporated into the path integral formalism.Comment: 25 pages, Latex, JHEP style, v4: revised for clarity without change in main contents, version to appear in JHE