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Field Theory and Statistical Mechanics are closely connected. A Wick rotation t ➝ i /(kT) will take you from one to the other.
http://jfi.uchicago.edu/~leop/TALKS/Phase%20TransitionsV2.4Dirac.pdf
* Tunneling phenomena are described most easily by performing a Wick rotation.
In flat space-time, the situation is well-understood: if your Hamiltonian has good positivity properties you can analytically continue to imaginary values of time, and when you do this you end up with “Euclidean” path integrals, which actually make sense, unlike QFT path integrals expressed on Minkowski space, which don’t. You can see the problem even in free field theory: the propagator is given by an integral that goes through two poles, so is ill-defined. The correct way to define it to get causal propagation for a theory with positive energies is to go above one pole, below the other, which is equivalent to “Wick rotating” the integration contour 90 degrees to lie on the imaginary time axis.
https://www.math.columbia.edu/~woit/wordpress/archives/000160.html