Functional integral representations of the Pauli-Fierz model with spin 1/2

Fumio Hiroshima, József Lorinczi

研究成果: Contribution to journalArticle査読

16 被引用数 (Scopus)

抄録

A Feynman-Kac-type formula for a Lévy and an infinite-dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of e- t HPF generated by the Pauli-Fierz Hamiltonian with spin 1/2 in non-relativistic quantum electrodynamics is constructed. When no external potential is applied HPF turns translation-invariant and it is decomposed as a direct integral HPF = ∫R3 HPF (P) d P. The functional integral representation of e- t HPF (P) is also given. Although all these Hamiltonians include spin, nevertheless the kernels obtained for the path measures are scalar rather than matrix expressions. As an application of the functional integral representations energy comparison inequalities are derived.

本文言語英語
ページ(範囲)2127-2185
ページ数59
ジャーナルJournal of Functional Analysis
254
8
DOI
出版ステータス出版済み - 4 15 2008

All Science Journal Classification (ASJC) codes

  • Analysis

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