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Ground states and spectrum of quantum electrodynamics of nonrelativistic particles


Author: Fumio Hiroshima
Journal: Trans. Amer. Math. Soc. 353 (2001), 4497-4528
MSC (1991): Primary 81Q10, 81U20, 47B15
DOI: https://doi.org/10.1090/S0002-9947-01-02719-2
Published electronically: June 14, 2001
MathSciNet review: 1851181
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Abstract:

A system consisting of finitely many nonrelativistic particles bound on an external potential and minimally coupled to a massless quantized radiation field without the dipole approximation is considered. An ultraviolet cut-off is imposed on the quantized radiation field. The Hamiltonian of the system is defined as a self-adjoint operator in a Hilbert space. The existence of the ground states of the Hamiltonian is established. It is shown that there exist asymptotic annihilation and creation operators. Hence the location of the absolutely continuous spectrum of the Hamiltonian is specified.


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Additional Information

Fumio Hiroshima
Affiliation: Institute of Applied Mathematics, University of Bonn, Wegelerstrasse 6, D53115 Bonn, Germany
Address at time of publication: Department of Mathematics and Physics, Setsunan University, Ikeda-naka-machi 17-8, 572-8508, Osaka, Japan
Email: hiroshima@mpg.setsunan.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-01-02719-2
Received by editor(s): August 14, 1998
Received by editor(s) in revised form: March 17, 2000
Published electronically: June 14, 2001
Additional Notes: This work was supported in part by Japan Society for the Promotion of Science (JSPS)
Article copyright: © Copyright 2001 American Mathematical Society

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