Spectral Analysis of the Dirac Polaron Spectral Analysis of the Dirac Polaron
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A system of a Dirac particle interacting with the radiation field is considered. The Hamiltonian of the system is defined by H = alpha . ((p) over cap - qA((x) over cap)) + m beta + H-f, where q is an element of R is a coupling constant, A((x) over cap) the quantized vector potential and H-f the free photon Hamiltonian. Since the total momentum is conserved, H is decomposed with respect to the total momentum with fiber Hamiltonian H(p) (p is an element of R-3). Since the self-adjoint operator H(p) is bounded from below, one can define the lowest energy E(p, m) := inf sigma(H(p)). We prove that E(p,m) is an eigenvalue of H(p) under the following conditions: (i) infrared regularization and (ii) E(p,m) < E(p, 0). We also discuss polarization vectors and the angular momentums.
- PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES 50(2), 307-339, 2014-06