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Thermal Green's Functions from Quantum Mechanical Path Integrals

In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational approach one avoids the loop-momentum integrals usually encountered in Feynman perturbation theory, although with thermal Green's functions, a discrete sum (over the winding numbers of paths with respect to the circular imaginary time) must be computed. The high-temperature expansion of this sum can be performed for all Green's functions at the same time, and is particularly simple for the static case. The procedure is illustrated by evaluating the two-point function to one-loop order in a $ϕ^3_6$ model.