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

Fumio Hiroshima, József Lorinczi

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2127-2185
Number of pages59
JournalJournal of Functional Analysis
Volume254
Issue number8
DOIs
Publication statusPublished - Apr 15 2008

All Science Journal Classification (ASJC) codes

  • Analysis

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