Action of the conformal group on steady state solutions to Maxwell’s equations and background radiation

  • Bertram KostantEmail author
  • Nolan R. Wallach
Part of the Progress in Mathematics book series (PM, volume 257)


The representation of the conformal group (PSU(2, 2)) on the space of solutions to Maxwell’s equations on the conformal compactification of Minkowski space is shown to break up into four irreducible unitarizable smooth Fréchet representations of moderate growth. An explicit inner product is defined on each representation. The energy spectrum of each of these representations is studied and related to plane wave solutions. The steady state solutions whose luminosity (energy) satisfies Planck’s Black Body Radiation Law are described in terms of this analysis. The unitary representations have notable properties. In particular they have positive or negative energy, they are of type \(A_{\mathfrak{q}}(\lambda )\) and are quaternionic. Physical implications of the results are explained.


Maxwell’s equations Conformal compactification Conformal group Unitary representations Background radiation 

Mathematics Subject Classification

78A25 58Z05 22E70 22E45 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsMITCambridgeUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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