Field Theory

Abstract

To motivate the study of field theory via the functional integral, we review the path integral of quantum mechanics, as discovered by Dirac [1] and Feynman [2]. We shall be brief and refer to the literature for many details because a number of excellent accounts (e.g. [3]) deal with this topic in depth (and because these details will not be required for understanding the rest of the text). The presentation given here is taken from [3]; it is included for the convenience of the reader and because, even though beautiful mathematical work has given a mathematically rigorous foundation for the functional integrals of quantum mechanics [3] and quantum field theory [6, 7, 5], many people still seem to believe that this is not the case. In fact, however, the Hamiltonian formalism of quantum field theory is so singular in more than two dimensions that the path integral seems a much better starting point.