相关论文: Cohomological Partition Functions for a Class of B…

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients.…

We investigate an equivariant generalization of Morse theory for a general class of integrable models. In particular, we derive equivariant versions of the classical Poincar\'e-Hopf and Gauss-Bonnet-Chern theorems and present the…

We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…

By means of the Minlos Theorem on support of cylindrical measures on vectorial topological spaces, we present several results on the rigorous definitions of Euclidean path integrals and applications to some problems on non-linear diffusion,…

We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization…

Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are {\it a priori}…

It is a common belief among field theorists that path integrals can be computed exactly only in a limited number of special cases, and that most of these cases are already known. However recent developments, which generalize the WKBJ method…

Path integral techniques in collective fields are shown to be a useful analytical tool to reformulate a field theory defined in terms of microscopic quark (gluon) degrees of freedom as an effective theory of collective boson (meson) fields.…

The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…

Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath…

The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier…

The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian…

We generalize the Generic Model Theorem for equivariant presheaves of structures; extending the results of Macintyre and Caicedo. We also introduce a new class of generic cohomologies and show how, for some examples, they simplify to non…

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general…

In this paper we outline the construction of semiclassical eigenfunctions of integrable models in terms of the semiclassical path integral for the Poisson sigma model with the target space being the phase space of the integrable system. The…

We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…

We prove a general form of the statement that the cohomology of a quotient stack can be computed by the Borel construction. It also applies to the lisse extensions of generalized cohomology theories like motivic cohomology and algebraic…

Simple bosonic path integral representation for path ordered exponent is derived. This representation is used, at first, to obtain new variant of non-Abelian Stokes theorem. Then new pure bosonic worldline path integral representations for…

In this article we review the Duistermaat-Heckman integration formula and the ensuing equivariant cohomology structure, in the finite dimensional case. In particular, we discuss the connection between equivariant cohomology and classical…

We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…