Distribution-theoretic methods in quantum field theory

SOM E HI S T OR Y . Singular generalized functions had been emerging in various applications (recall Dirac’s δ -function). Sobolev [1] found a systematic way to define such generalized functions as linear functionals on suitably chosen spaces of test functions. The most universally useful variant of the theory was suggested by Schwartz [2] (the so-called distributions; I will use the term interchangeably with generalized functions) who made a great effort to propagandize the simplicity and power of the technique of distributions [3] as did Gelfand and Shilov [4]. There is nothing inherently difficult in the idea of generalized function, and the theory can be taught in an almost elementary fashion [5]. Distributions ought to be taught to students early because of their wide usefulness (e.g. [3], [4], [6]).