Spectrum of the semi-relativistic Pauli-Fierz model I

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A HVZ type theorem for the semi-relativistic Pauli-Fierz Hamiltonian,H=(p⊗1-A)2+M2⊗1+V⊗1+1⊗Hf,M≥0, in quantum electrodynamics is studied. Here H is a self-adjoint operator in Hilbert space L2(Rd)⊗F≅∫Rd⊕Fdx, A=∫Rd⊕A(x)dx is a quantized radiation field and Hf is the free field Hamiltonian defined by the second quantization of a dispersion relation ω:Rd→R. It is emphasized that massless case, M=0, is included. Let E=inf σ(H) be the bottom of the spectrum of H. Suppose that the infimum of ω is m>0. Then it is shown that σess(H)=[E+m, ∞). In particular the existence of the ground state of H can be proven.

Original languageEnglish
Pages (from-to)330-349
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - May 1 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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