### Abstract

We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian H. There is no external potential and H fibers as ∫ H_{p}dp according to the total momentum p. We prove that the ground state subspace of H_{p} is two-fold degenerate provided the charge e and the total momentum p are sufficiently small. We also establish that the total angular momentum of the ground state subspace is ±1/2 and study the case of a confining external potential.

Original language | English |
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Pages (from-to) | 1091-1104 |

Number of pages | 14 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 5 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jan 1 2001 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)

### Cite this

*Advances in Theoretical and Mathematical Physics*,

*5*(6), 1091-1104. https://doi.org/10.4310/ATMP.2001.v5.n6.a4

**Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin.** / Hiroshima, Fumio; Spohn, H.

Research output: Contribution to journal › Article

*Advances in Theoretical and Mathematical Physics*, vol. 5, no. 6, pp. 1091-1104. https://doi.org/10.4310/ATMP.2001.v5.n6.a4

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TY - JOUR

T1 - Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin

AU - Hiroshima, Fumio

AU - Spohn, H.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian H. There is no external potential and H fibers as ∫ Hpdp according to the total momentum p. We prove that the ground state subspace of Hp is two-fold degenerate provided the charge e and the total momentum p are sufficiently small. We also establish that the total angular momentum of the ground state subspace is ±1/2 and study the case of a confining external potential.

AB - We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian H. There is no external potential and H fibers as ∫ Hpdp according to the total momentum p. We prove that the ground state subspace of Hp is two-fold degenerate provided the charge e and the total momentum p are sufficiently small. We also establish that the total angular momentum of the ground state subspace is ±1/2 and study the case of a confining external potential.

UR - http://www.scopus.com/inward/record.url?scp=12844255230&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12844255230&partnerID=8YFLogxK

U2 - 10.4310/ATMP.2001.v5.n6.a4

DO - 10.4310/ATMP.2001.v5.n6.a4

M3 - Article

AN - SCOPUS:12844255230

VL - 5

SP - 1091

EP - 1104

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 6

ER -