open access

https://hdl.handle.net/2115/13673

A particle-field Hamiltonian in relativistic quantum electrodynamics

英語

Hilbert spaces

2000-07

American Institute of Physics

Journal of Mathematical Physics

30(2)

512-520

We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space F:=[⊕^4^L^2(R^3)]⊗ F rad, where F rad is the Fock space of the quantized radiation field in the Coulomb gauge, V is an external potential in which the Dirac particle moves, g is a photon-momentum cutoff function in the interaction between the Dirac particle and the quantized radiation field, and τ∈R is a deformation parameter connecting the Hamiltonian with the "dipole approximation" (τ=0) and the original Hamiltonian (τ=1). We first discuss the self-adjointness problem of Htau(V,g). Then we consider Hτ:=Hτ(0,g), the Hamiltonian without the external potential. It is shown that, under a general condition on g, the closure of Hτ is unitarily equivalent to a direct integral ∫_R^3^⊕[overline Hτ(p)]dp with a fiber Hamiltonian Hτ(p) acting in the four direct sum ⊕^4Frad of Frad, physically the polaron Hamiltonian of the Dirac particle with total momentum p∈R^3.

学術雑誌論文

Version of Record

Copyright © 2000 American Institute of Physics

0022-2488

1089-7658