Bulletin of the Belgian Mathematical Society - Simon Stevin

The Fundamental Solution of the Hyperbolic Dirac Operator on $\mathbb{R}^{1,m}$ : a new approach

D. Eelbode and F. Sommen

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Abstract

In this paper, the fundamental solution of the Dirac equation on hyperbolic space will be calculated by means of the fundamental solution for the wave-operator in the $(m+1)$-dimensional Minkowski space-time of signature $(1,m)$. This leads to addition formulas for the fundamental solution in terms of the solution in a lower-dimensional Minkowski space-time. Certain identities between hypergeometric functions can then be used to obtain a closed form for the fundamental solution of the Dirac equation.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 1 (2005), 23-37.

Dates
First available in Project Euclid: 12 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1113318126

Digital Object Identifier
doi:10.36045/bbms/1113318126

Mathematical Reviews number (MathSciNet)
MR2134853

Zentralblatt MATH identifier
1072.30037

Subjects
Primary: 30G35: Functions of hypercomplex variables and generalized variables 33C05: Classical hypergeometric functions, $_2F_1$ 46F10: Operations with distributions

Keywords
Clifford analysis hyperbolic space hypergeometric functions

Citation

Eelbode, D.; Sommen, F. The Fundamental Solution of the Hyperbolic Dirac Operator on $\mathbb{R}^{1,m}$ : a new approach. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 1, 23--37. doi:10.36045/bbms/1113318126. https://projecteuclid.org/euclid.bbms/1113318126


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