### 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 language | English |
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Pages (from-to) | 4497-4528 |

Number of pages | 32 |

Journal | Transactions of the American Mathematical Society |

Volume | 353 |

Issue number | 11 |

Publication status | Published - Dec 1 2001 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 353, no. 11, pp. 4497-4528.

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TY - JOUR

T1 - Ground states and spectrum of quantum electrodynamics of nonrelativistic particles

AU - Hiroshima, Fumio

PY - 2001/12/1

Y1 - 2001/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041816242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041816242&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041816242

VL - 353

SP - 4497

EP - 4528

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 11

ER -