Feynman operator calculus: The constructive theory

DOI10.1016/j.exmath.2011.01.004zbMath1218.46052arXivmath-ph/0701039OpenAlexW2009050817MaRDI QIDQ534168

Tepper L. Gill, Woodford W. Zachary

Publication date: 17 May 2011

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0701039

zbMATH Keywords

Henstock-Kurzweil integralFeynman path integralHille-Yosida theorytime-ordered operator calculusTrotter-Kato theory

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds (46T12)

Cites Work

• The Dyson-Feynman conjectures
• Semigroups of linear operators and applications to partial differential equations
• Mathematical theory of Feynman path integrals
• On existence and non-existence of proper, regular, conditional distributions
• Feynman's operational calculus and evolution equations
• Decomposing the disentangling algebra on Wiener space
• Feynman path integrals for polynomially growing potentials
• Lectures in modern analysis and applications. II
• Functional integration
• ON THE CAUCHY PROBLEM ANDT-PRODUCTS FOR HYPOELLIPTIC SYSTEMS
• Time-ordered operators and Feynman–Dyson algebras
• Analytic representation of the square-root operator
• Foundations for relativistic quantum theory. I. Feynman’s operator calculus and the Dyson conjectures
• The Feynman Operator Calculus
• Operants: A Functional Calculus for Non-Commuting Operators
• Expansional in banach algebras
• The Radiation Theories of Tomonaga, Schwinger, and Feynman
• An Operator Calculus Having Applications in Quantum Electrodynamics
• Finitely Additive Measures
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