Functional Integrals and Adiabatic Limits in Field Theory

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Abstract
The behavior of a system of coupled fields as some of the particles become very heavy is investigated. By means of a technique expressing the relevant exact Green's functions as functional integrals, the limiting process need only be performed for bare one-particle propagators to get the result for the exact functions. It is shown that the resultant propagators are those for the remaining finite masses moving in external fields generated by the heavy particles acting as static point sources. The situation in which the coupling to the intermediate fields has no simple nonrelativistic limit is also discussed.

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