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

CRC Press eBooks

Feynman Integrals

Hui-Hsiung Kuo

Published May 4, 2018• 0 citations
Publisher

Abstract

In this chapter we will describe very briefly an important application of white noise distribution theory to Feynman integrals. This application was first discussed by Hida and Streit in [ 168 ]. We will explain the basic ideas of white noise approach to Feynman integrals and carry out explicit calculations for some simple cases. For recent developments, see de Falco and Khandekar [ 27 ], de Faria et al. [ 29 ], the book by Hida et al. [ 58 ], and Khandekar and Streit [ 79 ].

DOI
10.1201/9780203733813-14

Related papers

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

Mathematical Feynman Path Integrals and Their Applications

Sonia Mazzucchi

"Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added. This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists"--

WORLD SCIENTIFIC eBooks•Nov 7, 2019•3 citations

Feynman integrals as Hida distributions: the case of non-perturbative potentials

Martin Grothaus, Ludwig Streit, Anna Vogel

Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to time-dependent potentials. This involves an expectation w.r.t. a complex scaled Brownian motion. As examples polynomial potentials of degree $4n+2, n\in\mathbb N,$ and singular potentials of the form $\frac{1}{|x|^n}, n\in\mathbb N$ and $\frac{1}{x^n}, n\in\mathbb N,$ are worked out.

arXiv:0805.3253•May 21, 2008•4 citations

WHITE NOISE ANALYSIS: BACKGROUND AND A RECENT APPLICATION

Jeremy J. Becnel, Ambar N. Sengupta

We present a description of the framework of white noise analysis as an innite-dimensional distribution theory. We then describe some recent developments in the context of an application arising from quantum computing. 1.

QP-PQ, quantum probability and white noise analysis•Feb 1, 2008•2 citations

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

A white noise approach to phase space Feynman path integrals

Wolfgang Böck, M. 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.

arXiv:1012.1125•Theory of Probability and Mathematical Statistics•Jan 11, 2013•9 citations
In this chapter we will describe very briefly an important application of white noise distribution theory to Feynman integrals. This application was first discussed by Hida and Streit in [ 168 ]. We will explain the basic ideas of white noise approach to Feynman integrals and carry out explicit calculations for some simple cases. For recent developments, see de Falco and Khandekar [ 27 ], de Faria et al. [ 29 ], the book by Hida et al. [ 58 ], and Khandekar and Streit [ 79 ].
"Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added. This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists"--
Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to time-dependent potentials. This involves an expectation w.r.t. a complex scaled Brownian motion. As examples polynomial potentials of degree 4n+2,n∈N,4n+2, n\in\mathbb N,4n+2,n∈N, and singular potentials of the form 1∣x∣n,n∈N\frac{1}{|x|^n}, n\in\mathbb N∣x∣n1​,n∈N and 1xn,n∈N,\frac{1}{x^n}, n\in\mathbb N,xn1​,n∈N, are worked out.