Perturbation theory is used for approximate solutions from "summary" of The Quantum Theory of Fields by Steven Weinberg,Weinberg S
Perturbation theory is an essential tool in the physicist's arsenal. It allows us to tackle problems that are otherwise too difficult to solve exactly. The basic idea is straightforward: start with a system that we understand well, and then gradually introduce small changes, or perturbations, to see how the system responds. By treating these perturbations as small deviations from the known solution, we can make approximations that capture the essential physics without getting bogged down in the details. In quantum field theory, perturbation theory is particularly powerful. Here, we are dealing with systems that involve an infinite number of degrees of freedom, making exact solutions virtually impossible to find. Instead, we can start with a free theory, where interactions are turned off, and then systematically include terms that represent interactions between particles. These interactions are typically weaker tha...
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