### 抄録

By means of functional integrations spectral properties of semi-relativistic Pauli-Fierz HamiltoniansH=(p-αA)2+m2-m+V+Hrad in quantum electrodynamics are considered. Here p is the momentum operator, A a quantized radiation field on which an ultraviolet cutoff is imposed, V an external potential, _{Hrad} the free field Hamiltonian and m ≥ 0 describes the mass of electron. Two self-adjoint extensions of a semi-relativistic Pauli-Fierz Hamiltonian are defined. The Feynman-Kac type formula of ^{e -t H} is given. A self-adjointness, a spatial decay of bound states, a Gaussian domination of the ground state and the existence of a measure associated with the ground state are shown. All the results are independent of values of coupling constant α, and it is emphasized that m = 0 is included.

元の言語 | 英語 |
---|---|

ページ（範囲） | 784-840 |

ページ数 | 57 |

ジャーナル | Advances in Mathematics |

巻 | 259 |

DOI | |

出版物ステータス | 出版済み - 7 10 2014 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### これを引用

**Functional integral approach to semi-relativistic Pauli-Fierz models.** / Hiroshima, Fumio.

研究成果: ジャーナルへの寄稿 › 記事

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TY - JOUR

T1 - Functional integral approach to semi-relativistic Pauli-Fierz models

AU - Hiroshima, Fumio

PY - 2014/7/10

Y1 - 2014/7/10

N2 - By means of functional integrations spectral properties of semi-relativistic Pauli-Fierz HamiltoniansH=(p-αA)2+m2-m+V+Hrad in quantum electrodynamics are considered. Here p is the momentum operator, A a quantized radiation field on which an ultraviolet cutoff is imposed, V an external potential, Hrad the free field Hamiltonian and m ≥ 0 describes the mass of electron. Two self-adjoint extensions of a semi-relativistic Pauli-Fierz Hamiltonian are defined. The Feynman-Kac type formula of e -t H is given. A self-adjointness, a spatial decay of bound states, a Gaussian domination of the ground state and the existence of a measure associated with the ground state are shown. All the results are independent of values of coupling constant α, and it is emphasized that m = 0 is included.

AB - By means of functional integrations spectral properties of semi-relativistic Pauli-Fierz HamiltoniansH=(p-αA)2+m2-m+V+Hrad in quantum electrodynamics are considered. Here p is the momentum operator, A a quantized radiation field on which an ultraviolet cutoff is imposed, V an external potential, Hrad the free field Hamiltonian and m ≥ 0 describes the mass of electron. Two self-adjoint extensions of a semi-relativistic Pauli-Fierz Hamiltonian are defined. The Feynman-Kac type formula of e -t H is given. A self-adjointness, a spatial decay of bound states, a Gaussian domination of the ground state and the existence of a measure associated with the ground state are shown. All the results are independent of values of coupling constant α, and it is emphasized that m = 0 is included.

UR - http://www.scopus.com/inward/record.url?scp=84899989507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899989507&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2014.02.015

DO - 10.1016/j.aim.2014.02.015

M3 - Article

VL - 259

SP - 784

EP - 840

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -