### 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 language | English (US) |
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Pages (from-to) | 377-402 |

Number of pages | 26 |

Journal | Journal of Electromagnetic Waves and Applications |

Volume | 1 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

**Exact solution of the sommerfeld half-plane problem : a path integral approach without discretization.** / Ziolkowski, Richard W.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Exact solution of the sommerfeld half-plane problem

T2 - a path integral approach without discretization

AU - Ziolkowski, Richard W

PY - 1987/1/1

Y1 - 1987/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84947148971&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947148971&partnerID=8YFLogxK

U2 - 10.1163/156939387X00199

DO - 10.1163/156939387X00199

M3 - Article

VL - 1

SP - 377

EP - 402

JO - Journal of Electromagnetic Waves and Applications

JF - Journal of Electromagnetic Waves and Applications

SN - 0920-5071

IS - 4

ER -