Fumio Hiroshima and Jozsef Lorinczi 
Functional integral representation of the Pauli-Fierz model with spin 1/2
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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.