Localization of the number of photons of ground states in nonrelativistic QED

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Abstract

One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2(ℝ3) ⊗ F ≅ L2 (ℝ3; F), where F is the Boson Fock space over L2(ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to ∩k = 1D(1 ⊗ Nk), where N denotes the number operator of F. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ∥(1 ⊗ Nk/2ψg(x)∥F ≤ Dke-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular ψg ∈ ∩k = 1D(eβ|x|m+1 ⊗ Nk) for 0 < 0 < δ/2 is obtained.

Original languageEnglish
Pages (from-to)271-312
Number of pages42
JournalReviews in Mathematical Physics
Volume15
Issue number3
DOIs
Publication statusPublished - May 1 2003
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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