Complex-Distance Potential Theory and Hyperbolic Equations

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dc.creatorKaiser, Gerald
dc.date1999-08-31
dc.date1999-09-01
dc.date.accessioned2026-07-07T04:32:55Z
dc.date.available2026-07-07T04:32:55Z
dc.descriptionAn extension of potential theory in R^n is obtained by continuing the Euclidean distance function holomorphically to C^n. The resulting Newtonian potential is generated by an extended source distribution D(z) in C^n whose restriction to R^n is the delta function. This provides a natural model for extended particles in physics. In C^n, interpreted as complex spacetime, D(z) acts as a propagator generating solutions of the wave equation from their initial values. This gives a new connection between elliptic and hyperbolic equations that does not assume analyticity of the Cauchy data. Generalized to Clifford analysis, it induces a similar connection between solutions of elliptic and hyperbolic Dirac equations. There is a natural application to the time-dependent, inhomogeneous Dirac and Maxwell equations, and the `electromagnetic wavelets' introduced previously are an example.
dc.description25 pages, submited to Proceedings of 5th Intern. Conf. on Clifford Algebras, Ixtapa, June 24 - July 4, 1999
dc.identifierhttps://arxiv.org/abs/math-ph/9908031
dc.identifierhttp://arxiv.org/abs/math-ph/9908031
dc.identifierClifford Analysis, J. Ryan and W. Sprossig, eds., Birkhauser Progress in Physics, Vol. 19, 2000.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58380
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject31-XX, 32-XX, 35-XX, 78-XX
dc.titleComplex-Distance Potential Theory and Hyperbolic Equations
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