相关论文: Dependent coordinates in path integral measure fac…

The present work develops a framework to derive piecewise polynomial measures arising from invariant measures on adjoint orbits in the context of compact and semisimple Lie groups. These measures are computed from orbital integrals via…

We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the…

We prove a neat factorization property of Feynman graphs in covariant perturbation theory. The contribution of the graph to the effective action is written as a product of a massless scalar momentum integral that only depends on the basic…

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}…

Quantum many-body systems are characterized by patterns of correlations that define highly-non trivial manifolds when interpreted as data structures. Physical properties of phases and phase transitions are typically retrieved via simple…

We consider empirical measures in a triangular array setup with underlying distributions varying as sample size grows. We study asymptotic properties of multiple integrals with respect to normalized empirical measures. Limit theorems…

Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…

The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization…

In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…

We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…

Using noncommutative deformed canonical commutation relations, a model describing a noncommutative complex scalar field theory is considered. Using the path integral formalism, the noncommutative free and exact propagators are calculated to…

We discuss the limitations of the standard collinear approach. The kinematical approximations necessary to derive the collinear factorization are insufficient for the description of the exclusive final states. We argue that for a proper…

We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…

By means of the Ito-Nisio theorem, we introduce and discuss a general approach to series representations of path integrals. We then argue that the optimal basis for both ``primitive'' and partial averaged approaches is the Wiener…

Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is…

A matrix factorization problem is considered. The matrix to be factorized is algebraic, has dimension 2 X 2 and belongs to Moiseev's class. A new method of factorization is proposed. First, the matrix factorization problem is reduced to a…

We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries: the…

We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…

The Wigner function W(q,p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid…

The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially…