Abstract
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.
The first author extends birthday greetings to the second author Nolan Wallach. Nolan has been a long-time highly-valued friend and has been a brilliant, inspiring, and creative collaborator.
— From the first author
Research partially supported by NSF grant DMS 0963035.
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Notes
- 1.
Research partially supported by NSF grant DMS 0963035.
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Kostant, B., Wallach, N.R. (2014). Action of the conformal group on steady state solutions to Maxwell’s equations and background radiation. In: Howe, R., Hunziker, M., Willenbring, J. (eds) Symmetry: Representation Theory and Its Applications. Progress in Mathematics, vol 257. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-1590-3_14
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