2011-09-01, English, Article, Journal or magazine article edition: THE CHARACTERISTIC CAUCHY PROBLEM FOR DIRAC FIELDS ON CURVED BACKGROUNDS. HAfner, Dietrich; Nicolas, Jean-Philippe

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Physical Description
  • Magazine/​Journal article
Published
  • World Scientific Publishing Co. Pte Ltd., 2011 Sept
Language
  • English

Edition details

Title
  • THE CHARACTERISTIC CAUCHY PROBLEM FOR DIRAC FIELDS ON CURVED BACKGROUNDS.
Appears In
  • Journal of Hyperbolic Differential Equations, v.8, no.03, 2011 Sept, p.437 (ISSN: 0219-8916)
Author
  • HAfner, Dietrich
  • Nicolas, Jean-Philippe
Published
  • World Scientific Publishing Co. Pte Ltd., 2011 Sept
Physical Description
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http:/​/​dx.doi.org/​10.1142/​S0219891611002469 Byline: DIETRICH HAFNER, JEAN-PHILIPPE NICOLAS On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighborhood of the vertex. This is done for data in L.sup.2 and we give an explicit definition of the space of data on the light-cone producing a solution in H.sup.1. The method is based on energy estimates following Hormander [A remark on the characteristic Cauchy problem, J. Funct. Anal.93(2) (1990) 270--277]. The data for the characteristic Cauchy problem are only a half of the field, the other half is recovered from the characteristic data by integration of the constraints, consisting of the restriction of the Dirac equation to the cone. A precise analysis of the dynamics of light rays near the vertex of the cone is done in order to understand the integrability of the constraints; for this, the Geroch--Held--Penrose formalism is used.
Terms of Use
  • COPYRIGHT 2011 World Scientific Publishing Co. Pte Ltd.
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 462767713
  • 10.1142/​S0219891611002469

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