Ground state degeneracy of the Pauli-Fierz Hamiltonian inlcuding spin

2002/10/30 by F. Hiroshima, H. Spohn
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as Adv. Theor. Math. Phys. 5 (2001) 1091-1104 · See also http://www.intlpress.com/ATMP

arxiv created 2002/10/30 · arxiv updated 2009/11/30

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.

Related

• Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin
• Spectral Analysis of the Semi-relativistic Pauli-Fierz Hamiltonian
• Spectrum of the semi-relativistic Pauli-Fierz model II
• Quasi-classical Ground States. I. Linearly Coupled Pauli-Fierz Hamiltonians
• Non-relativistic Pauli--Fierz Hamiltonian for less than two photons