- #1
Iliody
- 25
- 5
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.
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√(p2+m2)}))
"=det(1+e^{-β√(p2+m2)}))",
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)
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√(p2+m2)}))
"=det(1+e^{-β√(p2+m2)}))",
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)