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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Ground states and spectrum of quantum electrodynamics of nonrelativistic particles
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by Fumio Hiroshima PDF
Trans. Amer. Math. Soc. 353 (2001), 4497-4528 Request permission

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
  • 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)
  • © Copyright 2001 American Mathematical Society
  • 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
  • MathSciNet review: 1851181