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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