Feynman's operational calculus and evolution equations

DOI10.1023/A:1005773828749zbMath0892.47018OpenAlexW1553866735MaRDI QIDQ1357515

Michel L. Lapidus, Brian DeFacio, Gerald W. Johnson

Publication date: 3 August 1998

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1005773828749

zbMATH Keywords

semigroups of operatorsFeynman path integraldisentanglingnoncommuting operatorsnonlocal potentialsFeynman's time-ordered operational calculusgeneralized path integralsums of noncommuting operators

Mathematics Subject Classification ID

Nuclear physics (81V35) One-parameter semigroups and linear evolution equations (47D06) Functional calculus for linear operators (47A60) Perturbation theory of linear operators (47A55) Path integrals in quantum mechanics (81S40) (n)-body potential quantum scattering theory (81U10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Applications of manifolds of mappings to the sciences (58D30) Linear integral equations (45A05)

Related Items (10)

Effects of absolute continuity in Feynman’s operational calculus ⋮ Feynman's operational calculus with arbitrary measures: an evolution equation in the general case and examples ⋮ Combining continuous and discrete phenomena for Feynman's operational calculus in the presence of a \((C_0)\) semigroup and Feynman-Kac formulas with Lebesgue-Stieltjes measures ⋮ Towards a comprehensive stability theory for Feynman's operational calculus: the time-dependent setting ⋮ Feynman operator calculus: The constructive theory ⋮ The Composition of Operator-Valued Measurable Functions is Measurable ⋮ Feynman's operational calculi: Disentangling away from the origin ⋮ Stability properties for Feynman's operational calculus in the combined continuous/discrete setting ⋮ Time dependent stability for Feynman's operational calculus ⋮ Towards a comprehensive stability theory for Feynman's operational calculus: the time independent setting

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