Spectral Analysis of the Semi-relativistic Pauli-Fierz Hamiltonian

Details Spectral Analysis of the Semi-relativistic Pauli-Fierz Hamiltonian Spectral Analysis of the Semi-relativistic Pauli-Fierz Hamiltonian

2008-05-30

arxiv.org/abs/0805.4776v1

Physics

Mathematical Physics

32 pages

Scientific paper

We consider a charged particle, spin 1/2, with relativistic kinetic energy and minimally coupled to the quantized Maxwell field. Since the total momentum is conserved, the Hamiltonian admits a fiber decomposition as $H(P)$, $P\in \BbbR^3$. We study the spectrum of $H(P)$. In particular we prove that, for non-zero photon mass, the ground state is exactly two-fold degenerate and separated by a gap, uniformly in $P$, from the rest of the spectrum.

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