01-407 Fumio Hiroshima and Herbert Spohn

Ground state degeneracy of the Pauli-Fierz Hamiltonian including spin (38K, Latex) Nov 5, 01

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Abstract. We consider an electron, spin $\han$, 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 $\int^\oplus \hp dp$ 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 $\pm\han$ and study the case of a confining external potential.

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