Fumio Hiroshima and Herbert Spohn
Ground state degeneracy of the Pauli-Fierz Hamiltonian including spin
(38K, Latex)
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.