Chapter four is fairly standard material, about what the theory looks like for free, non-interacting quanta, and the various procedures for getting there from either the Fock space formalism, or from quantizing classical theories. Since all of this is intended to be relativistically correct, there has to be no interference between points separated by space-like intervals, which constrains the commutation relations among the field operators. This leads naturally to representing scattering by a single operator, the S-matrix, which can be written as a kind of power series in terms of the interaction Hamiltonian . This demands a mess of algebra and book-keeping, the details of which absorb most books on field theory. Teller, however, goes over this very briskly before turning to the Feynman diagrams.
Every interaction is marked by a vertex.
The power lies, further, in the fact that one merely has to write down all topologically distinct diagrams representing the process in question in order to get all the terms to a given order for a process, with the number of vertices corresponding to the order in the S-matrix operator expansion.'' In other words, Feynman diagrams make quantum field theories useful for mere mortals, and the bulk of most QFT books is devoted to techniques for coaxing the most information out of diagrams or explaining different sets of Feynman rules belonging to different theories. The last chapter explains renormalization in twenty pages, assuming nothing more than an understanding of integration, and as such is a true tour de force of exposition. Since we never observe the bare mass, it is perhaps not completely illegitimate to make it take on whatever value is needed to fit experiment. But it gets worse. The effect of this is to make effective mass and charge depend on q, and so on the distance-scale at which particles interact.