Im working on deriving the final expression on the attached picture. The problem is that of a particle in a potential coupled to a "bath" of harmonic oscillators but I'm not sure how you arrive at the final expression. First of all, why are you allowed to assume that q is periodic on the interval [0,T(adsbygoogle = window.adsbygoogle || []).push({}); ^{-1}]? And secondly how should I use this? Should I plug in the fourier series expansion of q? And in that case what should I do with the integral in dt' (which I suppose has been transformed to an integral in τ by t'->-iτ)

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# Condensed matter problem with Feynman integral

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