The convergence of Gaussian path integrals over field configurations via Wick rotation is a rigorous mathematical procedure in Quantum Field Theory that transforms oscillatory Minkowski-space functional integrals into convergent Euclidean forms through analytic continuation to imaginary time. This mechanism relies on the formal definition of a Lorentzian metric signature change ($t \to -i\tau$), ensuring the exponential kernel decays rather than oscillates, thereby defining a well-posed probabilistic measure over field configurations in flat space-time. As a foundational theorem within statistical mechanics and high-energy physics, it provides the theoretical bridge between real-time dynamics and equilibrium partition functions without invoking specific computational examples or implementation details.
Prerequisite chain context: requires Generating Functionals in Path Integral Formulation.