The Feynman-Kac Formula with a Lebesgue-Stieltjes Measure and Feynman's Operational Calculus

DOI10.1002/sapm198776293zbMath0626.28008OpenAlexW2253557072MaRDI QIDQ3029240

Michel L. Lapidus

Publication date: 1987

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm198776293

zbMATH Keywords

Schrödinger equationFeynman-Kac formulaFeynman-Kac functionalFeynman diagramVolterra-Stieltjes integral equationFeynman path integralFeynman's operational calculusgeneralized Dyson series

Mathematics Subject Classification ID

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items

Feynman's operational calculus with arbitrary measures: an evolution equation in the general case and examples ⋮ The differential equation for the Feynman-Kac formula with a Lebesgue- Stieltjes measure ⋮ Noncommutative operations on Wiener functionals and Feynman's operational calculus ⋮ Moments of certain stochastic integrals occurring in mathematical physics ⋮ The Feynman integral and Feynman's operational calculus: A heuristic and mathematical introduction ⋮ A measure theoretic perspective on the space of Feynman diagrams ⋮ The Feynman-Kac formula with a Lebesgue-Stieltjes measure: An integral equation in the general case ⋮ An operational construction of the sum of two non-commuting observables in quantum theory and related constructions ⋮ 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 ⋮ Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture ⋮ Unnamed Item ⋮ A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula

Cites Work

• Operator valued measures and perturbations of semi-groups
• Perturbation theory and a dominated convergence theorem for Feynman integrals
• Product formula for imaginary resolvents with application to a modified Feynman integral
• The differential equation for the Feynman-Kac formula with a Lebesgue- Stieltjes measure
• Generalization of the Trotter-Lie formula
• Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman’s operational calculus
• Product formulas, nonlinear semigroups, and addition of unbounded operators
• Feynman Integrals and the Schrödinger Equation
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• The Radiation Theories of Tomonaga, Schwinger, and Feynman
• An Operator Calculus Having Applications in Quantum Electrodynamics
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