Embedded eigenvalues, localization and asymptotics of quantum field models: A functional integral approach

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Abstract

By means of functional integrals, a Hamiltonian of a system of a charged particle coupled to a quantized radiation field is investigated, it is the so called Pauli-Fierz model in nonrelativistic quantum electrodynamics. Embedded eigenvalues of the Hamiltonian with a singular external potential are studied and their multiplicities are estimated. The localization of a charge density of eigenvectors is considered. A partial trace of the semigroup generated by the Hamiltonian is defined and its classical limit, ℏ → 0, is discussed. Finally a nonrelativistic limit, c → ∞, is considered.

Original languageEnglish
Pages (from-to)351-375
Number of pages25
JournalJournal of Physics A: Mathematical and General
Volume35
Issue number2
DOIs
Publication statusPublished - Jan 18 2002
Externally publishedYes

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Hamiltonians
Functional Integral
Quantum Fields
eigenvalues
Eigenvalue
quantum electrodynamics
radiation distribution
Non-relativistic Limit
charged particles
eigenvectors
Classical Limit
Electrodynamics
Charged particles
Charge density
Eigenvalues and eigenfunctions
Eigenvector
Multiplicity
Semigroup
Trace
Radiation

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

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abstract = "By means of functional integrals, a Hamiltonian of a system of a charged particle coupled to a quantized radiation field is investigated, it is the so called Pauli-Fierz model in nonrelativistic quantum electrodynamics. Embedded eigenvalues of the Hamiltonian with a singular external potential are studied and their multiplicities are estimated. The localization of a charge density of eigenvectors is considered. A partial trace of the semigroup generated by the Hamiltonian is defined and its classical limit, ℏ → 0, is discussed. Finally a nonrelativistic limit, c → ∞, is considered.",
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AB - By means of functional integrals, a Hamiltonian of a system of a charged particle coupled to a quantized radiation field is investigated, it is the so called Pauli-Fierz model in nonrelativistic quantum electrodynamics. Embedded eigenvalues of the Hamiltonian with a singular external potential are studied and their multiplicities are estimated. The localization of a charge density of eigenvectors is considered. A partial trace of the semigroup generated by the Hamiltonian is defined and its classical limit, ℏ → 0, is discussed. Finally a nonrelativistic limit, c → ∞, is considered.

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