arXiv subjects
Publications and source records attributed to J. LaChapelle.
The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.
A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial differential equations with Dirichlet/Neumann boundary conditions. The construction is checked by evaluating several known kernels for regions with planar and spherical boundaries. Some new calculational techniques are introduced.
A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schrödinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette.
Super-matrix KdV and super-generalized non-linear Schrodinger equations are shown to arise from a symmetry reduction of ordinary self-dual Yang-Mills equations with supergauge groups