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

Fumio Hiroshima, József Lorinczi

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    22 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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