This is the first work in English to provide a comprehensive and rigorous account of an area of active recent research, in which a number of fundamental results have been obtained – and applied – not only by pure mathematicians but also by theoretical physicists investigating the quantum field. Heretofore, these results have been scattered piecemeal in periodicals, and the subject has been treated by parts in the monograph literature. This detailed presentation represents a compilation of these sources and, more than that, provides a systematic development of this complex field. Indeed, it has brought a vigorous and rapidly unfolded domain of study to formal maturity with an uncommon dispatch.
The careful presentation of preliminaries and the self-contained exposition of homology will be especially serviceable to the physicists, in whose hands this mathematical formalism should become a convenient and powerful tool for prying into the quantum realm. The author provides explicit applications of holomprphic functions to quantum field theory and to different equations with constant coefficients, among other subjects.
