### Abstract

A path integral constructed over a particular Riemann space is developed and applied to two-dimensional wedge problems. This path-integral-Riemann-space (PIRS) approach recovers the exact solutions of the heat conduction and the corresponding electromagnetic wedge problems. A high-frequency asymptotic evaluation of the PIRS electromagnetic wedge solution returns the standard geometrical theory of diffraction (GTD) results. Ramifications of this approach and its relationships with known path-integral methods are examined.

Original language | English (US) |
---|---|

Pages (from-to) | 2271-2281 |

Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 27 |

Issue number | 9 |

State | Published - 1986 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

**A path-integral-Riemann-space approach to the electromagnetic wedge diffraction problem.** / Ziolkowski, Richard W.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 27, no. 9, pp. 2271-2281.

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TY - JOUR

T1 - A path-integral-Riemann-space approach to the electromagnetic wedge diffraction problem

AU - Ziolkowski, Richard W

PY - 1986

Y1 - 1986

N2 - A path integral constructed over a particular Riemann space is developed and applied to two-dimensional wedge problems. This path-integral-Riemann-space (PIRS) approach recovers the exact solutions of the heat conduction and the corresponding electromagnetic wedge problems. A high-frequency asymptotic evaluation of the PIRS electromagnetic wedge solution returns the standard geometrical theory of diffraction (GTD) results. Ramifications of this approach and its relationships with known path-integral methods are examined.

AB - A path integral constructed over a particular Riemann space is developed and applied to two-dimensional wedge problems. This path-integral-Riemann-space (PIRS) approach recovers the exact solutions of the heat conduction and the corresponding electromagnetic wedge problems. A high-frequency asymptotic evaluation of the PIRS electromagnetic wedge solution returns the standard geometrical theory of diffraction (GTD) results. Ramifications of this approach and its relationships with known path-integral methods are examined.

UR - http://www.scopus.com/inward/record.url?scp=0010628897&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010628897&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0010628897

VL - 27

SP - 2271

EP - 2281

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

ER -