### Abstract

The spinless semi-relativistic Pauli-Fierz Hamiltonian H= (p o×1-A)^{2}+M^{2}+Vo× 1+1o×H_{f}, in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, H_{f} the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli-Fierz model with a fixed total momentum P ε^{d}: H(P) = s(P P _{f} - A(0))^{2} + M^{2} + H_{f}, M ≥ 0 is also proven for arbitrary P.

Original language | English |
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Article number | 1550015 |

Journal | Reviews in Mathematical Physics |

Volume | 27 |

Issue number | 7 |

DOIs | |

Publication status | Published - Aug 19 2015 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Reviews in Mathematical Physics*,

*27*(7), [1550015]. https://doi.org/10.1142/S0129055X15500154

**Self-adjointness of the semi-relativistic Pauli-Fierz Hamiltonian.** / Hidaka, Takeru; Hiroshima, Fumio.

Research output: Contribution to journal › Article

*Reviews in Mathematical Physics*, vol. 27, no. 7, 1550015. https://doi.org/10.1142/S0129055X15500154

}

TY - JOUR

T1 - Self-adjointness of the semi-relativistic Pauli-Fierz Hamiltonian

AU - Hidaka, Takeru

AU - Hiroshima, Fumio

PY - 2015/8/19

Y1 - 2015/8/19

N2 - The spinless semi-relativistic Pauli-Fierz Hamiltonian H= (p o×1-A)2+M2+Vo× 1+1o×Hf, in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hf the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli-Fierz model with a fixed total momentum P εd: H(P) = s(P P f - A(0))2 + M2 + Hf, M ≥ 0 is also proven for arbitrary P.

AB - The spinless semi-relativistic Pauli-Fierz Hamiltonian H= (p o×1-A)2+M2+Vo× 1+1o×Hf, in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hf the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli-Fierz model with a fixed total momentum P εd: H(P) = s(P P f - A(0))2 + M2 + Hf, M ≥ 0 is also proven for arbitrary P.

UR - http://www.scopus.com/inward/record.url?scp=84942036320&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942036320&partnerID=8YFLogxK

U2 - 10.1142/S0129055X15500154

DO - 10.1142/S0129055X15500154

M3 - Article

AN - SCOPUS:84942036320

VL - 27

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 7

M1 - 1550015

ER -