### 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 language | English |
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Pages (from-to) | 351-375 |

Number of pages | 25 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 35 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 18 2002 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

**Embedded eigenvalues, localization and asymptotics of quantum field models : A functional integral approach.** / Hiroshima, Fumio.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Embedded eigenvalues, localization and asymptotics of quantum field models

T2 - A functional integral approach

AU - Hiroshima, Fumio

PY - 2002/1/18

Y1 - 2002/1/18

N2 - 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.

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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UR - http://www.scopus.com/inward/citedby.url?scp=0037127180&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/35/2/313

DO - 10.1088/0305-4470/35/2/313

M3 - Article

AN - SCOPUS:0037127180

VL - 35

SP - 351

EP - 375

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 2

ER -