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