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Wick rotation : ウィキペディア英語版
Wick rotation

In physics, Wick rotation, named after Gian-Carlo Wick, is a method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation that substitutes an imaginary-number variable for a real-number variable. This transformation is also used to find solutions to problems in quantum mechanics and other areas.
==Overview==
Wick rotation is motivated by the observation that the Minkowski metric (with convention for the metric tensor)
:ds^2 = -(dt^2) + dx^2 + dy^2 + dz^2
and the four-dimensional Euclidean metric
:ds^2 = d\tau^2 + dx^2 + dy^2 + dz^2
are equivalent if one permits the coordinate to take on imaginary 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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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