The Schrödinger equation in quantum field theory

Abstract

Some aspects of the Schrodinger equation in quantum field theory are considered in this article. The emphasis is on the Schrodinger functional equation for Yang-Mills theory, arising mainly out of Feynman's work on (2+1)-dimensional Yang-Mills theory, which he studied with a view to explaining the confinement of gluons. The author extended Feynman's work in two earlier papers, and the present article is partly a review of Feynman's and the author's work and some further extension of the latter. The primary motivation of this article is to suggest that considering the Schrodinger functional equation in the context of Yang-Mills theory may contribute significantly to the solution of the confinement and related problems, an aspect which, in the author's opinion, has not received the attention it deserves. The relation of this problem with certain others such as those of quarks, superconductivity, and quantum gravity is considered briefly, together with certain basic aspects of the formalism that may be of interest in their own right, especially for the beginner.