Hi, I was studying for my final exam on statistical physics and a doubt raised on my head that was truly strong and disturbing (at least, for me), and that I couldn't answer to myself by now.(adsbygoogle = window.adsbygoogle || []).push({});

The doubt is: Given that we have in d dimensions a fermion non interacting gas, the statistical mechanics partition function will be

Z=∏_{p∈R^{d+1}, spin∈Z2}(1+e^{-β√(p^{2}+m^{2})}))

"=det(1+e^{-β√(p^{2}+m^{2})}))",

and in (d-1)+1 dimensions for a Dirac action will have as wick-rotated partition function

Z(β)=det(β(iγ⋅∂+m))

Are both related in some way?

I mean, they are systems with the same Hamiltonians, and given that there is a lot of analogies between the formalisms of QFT and statistical physics I though that both needed to be a little more similar...

Is there a relation between the two that I am not seeing? What's wrong with my intuition? I will be very grateful for any answer (if it isn't on the line of "Quantum Field Theory is a myth, the real thing is Aliens").

Sorry if this question was against the rules (I don't know for now if it could be).

(After posting this question here, I posted in phys*** st**kexc***ge, but I deleted from that place... Is that wrong? Sorry)

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# I Doubt about partition functions in QFT and in stat Mechanics

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