Exact solution of the sommerfeld half-plane problem

a path integral approach without discretization

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2 Citations (Scopus)

Abstract

The exact solution of the two-dimensional Sommerfeld half-plane problem is obtained with a path integral approach. The approach relies on the Riemann space associated with this problem but does not require discretization nor a transformation to the corresponding heat conduction problem. A new intrinsic symmetry property of the half-plane problem solutions is revealed and is connected to the characteristics of the underlying Riemann space. An endpoint rather than a stationary point argument reproduces Keller's GTD results from the path integral expression.

Original languageEnglish (US)
Pages (from-to)377-402
Number of pages26
JournalJournal of Electromagnetic Waves and Applications
Volume1
Issue number4
DOIs
StatePublished - Jan 1 1987
Externally publishedYes

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Riemann manifold
half planes
Heat conduction
conductive heat transfer
symmetry

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Physics and Astronomy(all)

Cite this

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abstract = "The exact solution of the two-dimensional Sommerfeld half-plane problem is obtained with a path integral approach. The approach relies on the Riemann space associated with this problem but does not require discretization nor a transformation to the corresponding heat conduction problem. A new intrinsic symmetry property of the half-plane problem solutions is revealed and is connected to the characteristics of the underlying Riemann space. An endpoint rather than a stationary point argument reproduces Keller's GTD results from the path integral expression.",
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