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Integral Transforms on Homogeneous Spaces of the de Sitter and Conformal Groups

  • P. Moylan

Abstract

Solutions to many problems in physics often invoke the use of integral transforms which are associated with certain invariance or transformation groups of the particular physical system under consideration. The most well-known example is the use of the Fourier transform in problems of non-relativistic and relativistic physics. There are other integral transforms which are also very useful. Fock’s solution to the bound state hydrogen atom problem1 uses an integral transform which is related, thru stereographic projection from S3 onto R3, to a Knapp-Stein intertwining operator2 of the associated SO0(1,4) transformation group of the problem.3 The Wightman function for a masseless scalar field is a kernel of an intertwining operator between two elementary representations (ERs) of the conformal group.4 We also wish to note the use of the Radon transform in problems of radiography.5

Keywords

Dirac Equation Homogeneous Space Stereographic Projection Conformal Group Riemannian Symmetric Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • P. Moylan
    • 1
  1. 1.Department of Science and MathematicsSaint Louis UniversityCahokiaUSA

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