Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1012.1125 · Theory of Probability and Mathematical Statistics

A white noise approach to phase space Feynman path integrals

Wolfgang Böck, M. Grothaus

Published Jan 11, 2013• 9 citations
arXivHTMLPDF

Abstract

The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schrödinger equation are obtained and the canonical commutation relations are satisfied. The latter can be shown, since we not only construct the integral but rather the Feynman integrand and the corresponding generating functional.

DOI
10.1090/s0094-9000-2013-00870-9

Related papers

A White Noise Approach to Phase Space Feynman Path Integrals

Wolfgang Böck, Martin Grothaus

The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schrödinger equation are obtained and the canonical commutation relations are satisfied. The latter can be shown, since we not only construct the integral but rather the Feynman integrand and the corresponding generating functional.

•Aug 17, 2016•18 citations

The Feynman integrand as a white noise distribution beyond perturbation theory

Martin Grothaus, Anna Vogel, Christopher Casenas Bernido +1 more

In this note the concepts of path integrals and techniques how to construct them are presented. Here we concentrate on a White Noise approach. Combining White Noise techniques with a generalized time‐dependent Doss' formula Feynman integrands are constructed as white noise distributions beyond perturbation theory.

AIP conference proceedings•Jan 1, 2008•4 citations

The Feynman integrand for the perturbed harmonic oscillator as a Hida distribution

Mario D. Cunha, Custódia Drumond, Peter Leukert +2 more

Abstract We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. We show that the Feynman integrand for the harmonic oscillator in an external potential is a Hida distribution.

arXiv:math-ph/0303005•Annalen der Physik•Jan 1, 1995•13 citations

Feynman path integrals in a phase space

Felix Alexandrovich Berezin

Feynman path integrals in a phase space are analyzed in detail. The analysis is based on the theory of operator symbols, in contrast with the traditional approach based on the direct use of canonical commutation relations. Particular attention is paid to the Weyl and Wick symbols, which are the most important in applications. The set of paths on which the integral is concentrated is studied. It is found that these paths are always discontinuous. This discontinuity is responsible for errors in certain papers on path integrals in a phase space. The most important properties of the Weyl and Wick symbols are reviewed.

Soviet Physics Uspekhi•Nov 30, 1980•107 citations

Randomized Hamiltonian Feynman integrals and Schrödinger-Itô stochastic equations

John Edward Gough, OLeg O Obrezkov, O G Smolyanov

In this paper, we consider stochastic Schroedinger equations with two-dimensional white noise. Such equations are used to describe the evolution of an open quantum system undergoing a process of continuous measurement. Representations are obtained for solutions of such equations using a generalization to the stochastic case of the classical construction of Feynman path integrals over trajectories in the phase space.

arXiv:1006.0640•Izvestiya Mathematics•Dec 31, 2005•6 citations

Phase space Feynman path integrals

Sergio A Albeverio, Giuseppina Guatteri, Sonia Mazzucchi

A rigorous mathematical formulation of the “phase space Feynman path integral” is given in a general setting. This is then applied to yield a representation of solutions of the Schrödinger equation with potential depending both on the position and momentum variables.

Journal of Mathematical Physics•Jun 1, 2002•36 citations
The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schrödinger equation are obtained and the canonical commutation relations are satisfied. The latter can be shown, since we not only construct the integral but rather the Feynman integrand and the corresponding generating functional.
Feynman path integrals in a phase space are analyzed in detail. The analysis is based on the theory of operator symbols, in contrast with the traditional approach based on the direct use of canonical commutation relations. Particular attention is paid to the Weyl and Wick symbols, which are the most important in applications. The set of paths on which the integral is concentrated is studied. It is found that these paths are always discontinuous. This discontinuity is responsible for errors in certain papers on path integrals in a phase space. The most important properties of the Weyl and Wick symbols are reviewed.