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The Schrödinger equation and the heat equation are also related by Wick rotation. However, there is a slight difference. Statistical mechanics n-point functions satisfy positivity whereas Wick-rotated quantum field theories satisfy reflection positivity.
It is called a rotation because when we represent complex numbers as a plane, the multiplication of a complex number by i is equivalent to rotating the vector representing that number by an angle of about the origin.
When Stephen Hawking wrote about "imaginary time" in his famous book A Brief History of Time, he was referring to Wick rotation.
Wick rotation also relates a QFT at a finite inverse temperature β to a statistical mechanical model over the "tube" R3×S1 with the imaginary time coordinate τ being periodic with period β.
Note, however, that the Wick rotation cannot be viewed as a rotation on a complex vector space that is equipped with the conventional norm and metric induced by the inner product, as in this case the rotation would cancel out and have no effect at all.
Read more about this topic: Wick Rotation