Abstract
The semigroup of statistical operators, and the unitary group of time translation operators generated by the same Hamiltonian of a nonrelativistic fermion field, are naturally imbedded in a holomorphic half-plane semigroup. The statistical expectation values of products of time-dependent operators are then boundary values of holomorphic functions which allow a Bochner integral representation with a Cauchy kernel. The general time-temperature-dependent Green's functions permit a concise spectral representation. It is suggested that a thermodynamic perturbation theory should treat the Heisenberg and Bloch equations simultaneously in terms of a perturbation theory for holomorphic half-plane semigroups generated by semibounded self-adjoint Hamiltonians.
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