Path integrals play an important role in modern quantum field theory. One usually first encounters them as useful formal devices to derive Feynman rules. For gauge theories they yield straightforwardly the Ward identities. Namely, if BRST symmetry (the “quantum gauge invariance” discovered by Becchi, Rouet, Stora and Tyutin) holds at the quantum level, certain relations between Green functions can be derived from path integrals, but details of the path integral (for example, the precise form of the measure) are not needed for this purpose. Once the BRST Ward identities for gauge theories have been derived, unitarity and renormalizability can be proven, and at this point one may forget about path integrals if one is only interested in perturbative aspects of quantum field theories. One can compute higher-loop Feynman graphs without ever using path integrals.

However, for nonperturbative aspects, path integrals are essential. The first place where one encounters path integrals in nonperturbative quantum field theory is in the study of instantons and solitons. Here advanced methods based on path integrals have been developed. For example, in the case of instantons the correct measure for integration over their collective coordinates (corresponding to the zero modes) is needed. In particular, for supersymmetric nonabelian gauge theories, there are only contributions from these zero modes, while the contributions from the nonzero modes cancel between bosons and fermions.