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

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journal contribution
posted on 13.02.2017, 15:57 by Fumio Hiroshima, Jozsef Lorinczi
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−tHPF 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)dP. The functional integral representation of e−tHPF(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.

Funding

This work is financially supported by Grant-in-Aid for Science Research (C) 17540181 from JSPS.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

J. Funct. Anal.

Volume

254

Pages

2127 - 2185

Citation

HIROSHIMA, F. and LORINCZI, J., 2008. Functional integral representations of the Pauli-Fierz model with spin 1/2. Journal of Functional Analysis, 254 (8), pp.2127-2185.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2008

ISSN

0022-1236

Language

en