"After reviewing some basic principles of quantum field theory in Chapter 1, we now turn to a series of problems exploring various aspects of functional methods. Although it lacks a robust mathematical foundation in the case of interacting theories (but the situation in this respect is no better within the canonical formalism), the formulation of QFT in terms of path integrals considerably simplifies many manipulations that would otherwise be extremely tedious because of the need to keep track of the ordering of operators.

Besides the conventional representation of expectation values of time-ordered products of field operators and their generating functionals in terms of path integrals, we also briefly discuss the worldline representation for propagators and for one-loop effective actions, which provides an alternative point of view on quantization. Moreover, these ideas are not limited to ordering products of field operators, and can be useful in managing products of other types of non-commuting objects."