Ground states and spectrum of quantum electrodynamics of nonrelativistic particles

Research output: Contribution to journalArticle

17 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)4497-4528
Number of pages32
JournalTransactions of the American Mathematical Society
Volume353
Issue number11
Publication statusPublished - Dec 1 2001

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Hamiltonians
Electrodynamics
Ground state
Ground State
Radiation
Creation Operators
Absolutely Continuous Spectrum
Hilbert spaces
Self-adjoint Operator
Annihilation
Ultraviolet
Dipole
Mathematical operators
Hilbert space
Approximation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Ground states and spectrum of quantum electrodynamics of nonrelativistic particles. / Hiroshima, Fumio.

In: Transactions of the American Mathematical Society, Vol. 353, No. 11, 01.12.2001, p. 4497-4528.

Research output: Contribution to journalArticle

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