**
Below is the ascii version of the abstract for 07-137.
The html version should be ready soon.**Fumio Hiroshima and Jozsef Lorinczi
Functional integral representation of the Pauli-Fierz model with spin 1/2
(666K, pdf)
ABSTRACT. A Feynman-Kac-type formula for a L\'evy 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.