Regularized, continuum Yang-Mills process and Feynman-Kac functional integral

A Feynman-Kac Path-Integral Implementation for Poisson's Equation

This study presents a Feynman-Kac path-integral implementation for solving the Dirichlet problem for Poisson’s equation. The algorithm is a modified “walk on spheres” (WOS) that includes the FeynmanKac path-integral contribution for the source term. In our approach, we use the Poisson kernel instead of simulating Brownian trajectories in detail to implement the path-integral computation. We der...

Feynman Rules in N = 2 projective superspace III : Yang - Mills

The kinetic action of the N = 2 Yang-Mills vector multiplet can be written in projective N = 2 superspace using projective multiplets. It is possible to perform a simple N = 2 gauge fixing, which translated to N = 1 component language makes the kinetic terms of gauge potentials invertible. After coupling the Yang-Mills multiplet to unconstrained sources it is very simple to integrate out the ga...

Quantum Feynman-Kac perturbations

The Feynman-Kac formula

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...

Functional derivatives Schrödinger equations and Feynman integral

Cutoff Schrödinger equations in functional derivatives are solved via quantized Galerkin limit of antinormal functional Feynman integrals for Schrödinger equations in partial derivatives. Mathematics Subject Classification 2000: 81T08, 81T16; 26E15, 81Q05, 81S40.