The Wick Rotation is a rigorous mathematical procedure in quantum field theory and statistical mechanics that establishes a conformal mapping between Lorentzian manifolds with Minkowski signature and Euclidean spaces via the analytic continuation $t \to -i\tau$. This transformation rotates the time coordinate into an imaginary dimension, converting the oscillatory exponential factors of the path integral ($e^{iS}$) into decaying real exponentials ($e^{-S_E}$), thereby transforming a unitary quantum mechanical system into a non-unitary statistical field theory. By rigorously defining this analytic continuation within the context of complex time domains, the method resolves singularities in perturbation series and enables the application of standard Euclidean functional integration techniques to relativistic systems defined on flat spacetime.
Prerequisite chain context: requires Convergence of Gaussian Path Integrals over Field Configurations via Wick Rotation.