Everything else
Tom Banks · 2008
In addition to the big omissions I mentioned in the text, there is a host of subjects in field theory that I have neglected. I will mention them here, without detailed reference. In the days of Spires and Google detailed reference hardly seems necessary: all you need is a name. The large- N approximation, particularly the connection between large- N matrix field theories and string theory, is a big lacuna. I've barely mentioned the field of computational lattice gauge theory, which is slowly achieving a quantitative understanding of the hadron spectrum and other low-energy properties of QCD. The use of field theory techniques in condensed-matter physics produced the theory of superconductivity, of critical phenomena, and of the quantum Hall effect as well as a variety of other phenomena. The books by Parisi, Ma, Drouffe and Itzykson, and Zinn-Justin provide an entrée into this vast body of knowledge. Another big lacuna is the study of integrable two-dimensional theories and exact S-matrices. There has been a variety of attempts to study the high-energy fixed-momentum-transfer region of scattering amplitudes (the Regge region) by summing selected classes of diagrams in field theory. This has led to an effective field theory approach called Reggeon calculus as well as to a very interesting set of equations called the BFKL equations (this is not quite the Regge region). Then there is the use of two-dimensional conformal field theory to do perturbative string theory.