Product formula for imaginary resolvents with application to a modified Feynman integral

DOI10.1016/0022-1236(85)90088-6zbMath0601.47025OpenAlexW2010375821MaRDI QIDQ1081099

Michel L. Lapidus

Publication date: 1985

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(85)90088-6

zbMATH Keywords

convergenceSchrödinger equationmodified Feynman integralpair of self-adjoint operatorsproduct formula for imaginary resolventsTrotter-Lie formula

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Groups and semigroups of linear operators (47D03) Path integrals in quantum mechanics (81S40) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items

The Trotter-Kato product formula for Gibbs semigroups ⋮ The analytic operator-valued Feynman integral via additive functionals of Brownian motion ⋮ Path reparametrization in a path integral on a finite-dimensional manifold ⋮ Two approaches to the use of unbounded operators in Feynman's operational calculus ⋮ The Trotter–Lie product formula for Gibbs semigroups ⋮ A dominated-type convergence theorem for the Feynman integral ⋮ The Feynman-Kac Formula with a Lebesgue-Stieltjes Measure and Feynman's Operational Calculus ⋮ Remarks on the Trotter-Kato product formula for unitary groups ⋮ Product Formula for Resolvents of Normal Operators and the Modified Feynman Integral ⋮ Unnamed Item

Cites Work

• Analysis of the Laplacian on a complete Riemannian manifold
• A product formula and its application to the Schrödinger equation
• Notes on the Feynman integral. III: The Schrödinger equation
• Generalization of the Trotter-Lie formula
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Kernels of elliptic operators: bounds and summability
• Mathematical theory of Feynman path integrals
• Remarks on the Schrödinger operator with singular complex potentials
• The product formula for semigroups defined by Friedrichs extensions
• Schrödinger semigroups
• On the Product of Semi-Groups of Operators
• Product formulas, nonlinear semigroups, and addition of unbounded operators
• Feynman Integrals and the Schrödinger Equation
• The Trotter product formula for perturbations of semibounded operators
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item