"Wick rotation is a very basic procedure for inter-playing Lorentzian and Riemannian geometry. The simplest example applies to \mathbb R^{n+1} endowed with both the standard Minkowski metric {-dx_0}^2+\cdots+dx_{n-1}^2+dx_n^2\, and the Euclidean metric dx_0^2+\cdots+dx_n^2\,. By definition ... these are related via a Wick rotation directed by the vector field \frac{\partial}{\partial x_0}. Sometimes one refers to it as "passing to the imaginary time"."