 07137 Fumio Hiroshima and Jozsef Lorinczi
 Functional integral representation of the PauliFierz model with spin 1/2
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Jun 5, 07

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Abstract. A FeynmanKactype 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 PauliFierz
Hamiltonian with spin $\han$ in nonrelativistic 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.
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