On the Spectral Analysis of Quantum Electrodynamics with Spatial Cutoffs. I

Details On the Spectral Analysis of Quantum Electrodynamics with Spatial Cutoffs. I On the Spectral Analysis of Quantum Electrodynamics with Spatial Cutoffs. I

2008-12-18

arxiv.org/abs/0812.3482v1

Physics

Mathematical Physics

Scientific paper

In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground state for sufficiently small values of coupling constants. The spectral scattering theory is studied as well and it is shown that asymptotic fields exist and the spectral gap is closed.

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