相关论文: A Stochastic Approach to the Definition of the Pat…

Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…

We present a way for calculating the Lagrangian path integral measure directly from the Hamiltonian Schwinger--Dyson equations. The method agrees with the usual way of deriving the measure, however it may be applied to all theories, even…

Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrised field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary,…

We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…

We establish a direct connection between the Feynman-Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics. By considering a generalized influence functional in the strong…

We develop a general framework for pathwise stochastic integration that extends F\"ollmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums and provides pathwise counterparts of It\^o, Stratonovich,…

By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…

Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…

Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels…

We give two novel proofs that the path integral and stochastic quantizations of generic scalar Euclidean quantum field theories are equivalent. Our proofs rely on Taylor interpolations indexed by forests, in the fashion of constructive…

We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…

Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them…

We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a…

Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…

Feynman's Lagrangian path integral was an outgrowth of Dirac's vague surmise that Lagrangians have a role in quantum mechanics. Lagrangians implicitly incorporate Hamilton's first equation of motion, so their use contravenes the uncertainty…

We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation…

A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by Lagrangian formalism suffers problems due to the lack of geometrical structure of the configuration space…

Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…

A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…

Two problems are addressed for the path of certain stochastic processes: a) do they define currents? b) are these currents of a classical type? A general answer to question a) is given for processes like semimartingales or with Lyons-Zheng…