Spectral analysis of the semi-relativistic Pauli-Fierz hamiltonian

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We consider a charged particle, spin frac(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 ∈ R3. 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. © 2008 Elsevier Inc. All rights reserved.




Miyao, T., & Spohn, H. (2009). Spectral analysis of the semi-relativistic Pauli-Fierz hamiltonian. Journal of Functional Analysis, 256(7), 2123–2156. https://doi.org/10.1016/j.jfa.2008.09.014

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