# Potential theory, path integrals and the Laplacian of the indicator

@article{Lange2012PotentialTP,
title={Potential theory, path integrals and the Laplacian of the indicator},
author={Rutger-Jan Lange},
journal={Journal of High Energy Physics},
year={2012},
volume={2012},
pages={1-46}
}
• Rutger-Jan Lange
• Published 8 November 2012
• Mathematics
• Journal of High Energy Physics
A bstractThis paper links the field of potential theory — i.e. the Dirichlet and Neumann problems for the heat and Laplace equation — to that of the Feynman path integral, by postulating the following seemingly ill-defined potential:$V(x):=\mp \frac{{{\sigma^2}}}{2}\nabla_x^2{1_{{x\in D}}}$where the volatility is the reciprocal of the mass (i.e. m = 1/σ2) and ħ = 1. The Laplacian of the indicator can be interpreted using the theory of distributions: it is the d-dimensional analogue of the…
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