Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin

Fumio Hiroshima, H. Spohn

Research output: Contribution to journalArticle

23 Citations (Scopus)

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 ∫ 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.

Original languageEnglish
Pages (from-to)1091-1104
Number of pages14
JournalAdvances in Theoretical and Mathematical Physics
Volume5
Issue number6
DOIs
Publication statusPublished - Jan 1 2001

Fingerprint

Degeneracy
Ground State
momentum
ground state
Momentum
Subspace
confining
electron spin
radiation distribution
angular momentum
Angular Momentum
fibers
Fold
approximation
Radiation
Charge
Fiber
Electron
Approximation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

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

In: Advances in Theoretical and Mathematical Physics, Vol. 5, No. 6, 01.01.2001, p. 1091-1104.

Research output: Contribution to journalArticle

@article{33752cd4ce724ac2b4a35e6ea60f1f21,
title = "Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin",
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 ∫ 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.",
author = "Fumio Hiroshima and H. Spohn",
year = "2001",
month = "1",
day = "1",
doi = "10.4310/ATMP.2001.v5.n6.a4",
language = "English",
volume = "5",
pages = "1091--1104",
journal = "Advances in Theoretical and Mathematical Physics",
issn = "1095-0761",
publisher = "International Press of Boston, Inc.",
number = "6",

}

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 -