Wick Rotation - Overview

Overview

It is motivated by the observation that the Minkowski metric (with (−1, +1, +1, +1) convention for the metric tensor)

and the four-dimensional Euclidean metric

are equivalent if one permits the coordinate t to take on imaginary values. The Minkowski metric becomes Euclidean when t is restricted to the imaginary axis, and vice versa. Taking a problem expressed in Minkowski space with coordinates x, y, z, t, and substituting, sometimes yields a problem in real Euclidean coordinates x, y, z, which is easier to solve. This solution may then, under reverse substitution, yield a solution to the original problem.