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| CATEGORIES ABOUT WICK ROTATION | |
| quantum field theory | |
| statistical mechanics | |
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It is motivated by the observation that the Minkowski Metric : and the four-dimensional Euclidean metric : are not distinct if one permits the coordinate to take on Complex values. The Minkowski metric becomes Euclidean when is restricted to the Imaginary Axis , and vice versa. Taking a problem expressed in Minkowski space with coordinates , and substituting , sometimes yields a problem in real Euclidean coordinates which is easier to solve. This solution may then, under reverse substitution, yield a solution to the original problem. Wick rotation connects Quantum Mechanics to Statistical Mechanics in a surprising way. The Schrödinger Equation and the Heat Equation are related by Wick rotation, for example. The reasons for this are not understood. Wick rotation is named after Gian-Carlo Wick . It is called a ''rotation'' because when we represent complex numbers as a plane, the multiplication of a complex number by is equivalent to rotating the Vector representing that number by an Angle of . 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. SEE ALSO |
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