Feynman rule in finite volume or at periodic boundary condition

Question

Dear all,

I am wondering, whether the Wick theorem for free particles (in the form: $n$-point correlators split into $2$-point correlators) also hold for particles in a finite volume or for particles on a circle (periodic boundary conditions)? Or are there controlled extra terms?

I was curious to derive a set of Feynman rules for a quantum mechanical particle (not yet a field) in some potential etc, in either of the two settings.

PS: I might add I would be also interested to see any finite or periodic analogon of the harmonic oscillator, for which again Wicks theorem holds, so I can use it as the underlying free theory for deriving Feynman rules.

I am very sure that many people have thought about this before, but I have a hard time finding literature on it. Any hint would be much appreciated :-)

Greetings,
Simon