Functional Integral Representation of the Pauli-Fierz Model with Spin 1/2

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dc.creatorHiroshima, Fumio
dc.creatorLorinczi, Jozsef
dc.date2007-06-06
dc.date2008-01-16
dc.date.accessioned2026-07-07T08:54:26Z
dc.date.available2026-07-07T08:54:26Z
dc.descriptionA 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 $e^{-t\PF}$ generated by the Pauli-Fierz Hamiltonian with spin $\han$ in non-relativistic quantum electrodynamics is constructed. When no external potential is applied $\PF$ turns translation invariant and it is decomposed as a direct integral $\PF = \int_\BR^\oplus \PF(P) dP$. The functional integral representation of $e^{-t\PF(P)}$ 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.
dc.descriptionThis is a revised version. This paper will be published from J. Funct. Anal
dc.identifierhttps://arxiv.org/abs/0706.0833
dc.identifierhttp://arxiv.org/abs/0706.0833
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145929
dc.subjectMathematical Physics
dc.titleFunctional Integral Representation of the Pauli-Fierz Model with Spin 1/2
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