Abstract: | The definition of an infinite-dimensional, or functional, integral is discussed, and methods are given for the evaluation of certain types of functional integrals. A technique is described for the derivat10n of a partial differential equation satisfied by the distribution of values of the functions in the space to be integrated over, and the relation of this distribution to certain forms of functional integrals is discussed. A generalization of a theorem of Cameron and Martin is given, and possible numerical techniques for the evaluation of functional integrals are discussed.
A specific representation for the ground state functional of a non-linear model of a quantum field theory is given. A Gaussian approximation for the ground state functional is computed by the Ritz variational method. using a lattice of cells in ordinary space. The relation between the physical mass of the particles described, the cell size, and the unrenormal1zed mass and coupling constant is discussed. The ground state functional is also expanded in a perturbation series, and various divergent terms which appear are compared with terms in the standard Feynman Dyson perturbation scheme. |