The core principle posits that Quantum Field Theory (QFT) for free scalar fields is formulated via path integrals over field configurations weighted by the exponential of the action, rendering Lorentz variance manifest and simplifying gauge theory quantization. This approach utilizes Gaussian functional integration identities to derive generating functionals from which time-ordered correlation functions are obtained through functional differentiation with respect to external sources. The resulting Feynman propagator in momentum space is defined as $i/(p^2 - m^2 + i\epsilon)$, where the specific pole prescription arises naturally from analytic continuation between real-time and Euclidean signatures via Wick rotation.
The core principle posits that Quantum Field Theory (QFT) for free scalar fields is formulated via path integrals over field configurations weighted by the exponential of the action, rendering Lorent…