Ground state degeneracy of the Pauli-Fierz Hamiltonian inlcuding 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 ${\int }^{\oplus }{H}_{p}dp$ 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 $\pm 1/2$ and study the case of a confining external potential.

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