Ground state degeneracy of the Pauli-Fierz Hamiltonian inlcuding spin

Details Ground state degeneracy of the Pauli-Fierz Hamiltonian inlcuding spin Ground state degeneracy of the Pauli-Fierz Hamiltonian inlcuding spin

2002-10-30

arxiv.org/abs/math-ph/0210052v1

Adv. Theor. Math. Phys. 5 (2001) 1091-1104

Physics

Mathematical Physics

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Scientific paper

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 $\int^\oplus H_p dp$ 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 $\pm1/2$ and study the case of a confining external potential.

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