Generalized Eigenvectors and Group Representations — The Connection Between Representations of SO(4, l) and the Poincaré Group

  • A. Böhm
Chapter
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 1)

Abstract

Rarely has a mathematical structure been so eagerly accepted by physicists as the Rigged Hilbert Space \(\Phi \subset H \subset \Phi ^X\). The main reason for this is probably its ability to elevate the Dirac formalism of quantum mechanic that is “scarcely to be surpassed in brevity and elegance” (v. Neumann) into an equally beautiful and mathematically rigorous theory. Furthermore, the Rigged Hilbert Space is an important means of investigating such mathematical structures as representations of non-compact groups which have become very important in theoretical physics. The employment of the R. H. Sp. provides the possibility for working with algebraic (infinitesimal) methods in the representation theory of non-compact groups, which are so familiar to physicists from compact group representations.

Keywords

Irreducible Representation Unitary Representation Unitary Irreducible Representation Generalize Eigenvector Poincare Group 
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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References and Footnotes

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Copyright information

© D. Reidel Publishing Company 1973

Authors and Affiliations

  • A. Böhm
    • 1
  1. 1.University of TexasAustinUSA

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