Condensed matter problem with Feynman integral

1. Apr 28, 2015

aaaa202

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-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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2. Apr 29, 2015

DrDu

Did you have a look on how the Matsubara formalism works, e.g. in Fetter/ Valecka?