On three magnetic relativistic Schrödinger operators and imaginary-time path integrals

DOI10.1007/s11005-012-0573-6zbMath1296.81025OpenAlexW2076182800MaRDI QIDQ692863

Takashi Ichinose

Publication date: 6 December 2012

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-012-0573-6

zbMATH Keywords

path integralquantizationFeynman-Kac formulaLévy processpseudo-differential operatorsrelativistic Schrödinger operatorFeynman-Kac-Itô formulaimaginary-time path integral

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) PDEs in connection with relativity and gravitational theory (35Q75)

Related Items (2)

A third representation of Feynman-Kac-Itô formula with singular magnetic vector potential ⋮ The zero-mass limit problem for a relativistic spinless particle in an electromagnetic field

Cites Work

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• Unicity of the integrated density of states for relativistic Schrödinger operators with regular magnetic fields and singular electric potentials
• Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field
• Spectra of relativistic Schrödinger operators with magnetic vector potentials
• Magnetic pseudodifferential operators
• Exponential product approximation to the integral kernel of the Schrödinger semigroup and to the heat kernel of the Dirichlet Laplacian
• On the relativistic Feynman-Kac-Ito formula
• Lévy Processes and Stochastic Calculus
• The Stability of Matter in Quantum Mechanics
• Sharp Error Bound on Norm Convergence of Exponential Product Formula and Approximation to Kernels of Schrödinger Semigroups
• Functional Analysis
• The norm convergence of the Trotter-Kato product formula with error bound
• Note on the paper: ``The norm convergence of the Trotter--Kato product formula with error bound by T. Ichinose and H. Tamura.

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