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2019 A new class of Volterra-type integral equations from relativistic quantum physics
Matthias Lienert, Roderich Tumulka
J. Integral Equations Applications 31(4): 535-569 (2019). DOI: 10.1216/JIE-2019-31-4-535

Abstract

We study a new kind of linear integral equations for a relativistic quantum-mechanical two-particle wave function $\psi (x_1,x_2)$, where $x_1,x_2$ are spacetime points. In the case of retarded interaction, these integral equations are of Volterra-type in the in the time variables, i.e., they involve a time integration from 0 to $t_i = x_i^0, i=1,2$. They are interesting not only in view of their applications in physics, but also because of the following mathematical features: (a) time and space variables are more interrelated than in normal time-dependent problems, (b) the integral kernels are singular, and the structure of these singularities is non-trivial, (c) they feature time delay. We formulate a number of examples of such equations for scalar wave functions and prove existence and uniqueness of solutions for them. We also point out open mathematical problems.

Citation

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Matthias Lienert. Roderich Tumulka. "A new class of Volterra-type integral equations from relativistic quantum physics." J. Integral Equations Applications 31 (4) 535 - 569, 2019. https://doi.org/10.1216/JIE-2019-31-4-535

Information

Published: 2019
First available in Project Euclid: 6 February 2020

zbMATH: 07169460
MathSciNet: MR4060439
Digital Object Identifier: 10.1216/JIE-2019-31-4-535

Subjects:
Primary: 45D05
Secondary: 45E99, 81Q40

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.31 • No. 4 • 2019
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