Algebraic Structures of Degenerate Systems, Physical Requirements and the Indefinite Metric

  • Hendrik Grundling
  • C. A. Hurst


The basic algebraic structures of systems with a gauge degeneracy have been developed in a C’ - algebra framework in [1], of which the present work is a natural extension. We consider the treatment of algebraic conditions in more detail, as well as the compatibility conditions between a given constraint set and a given set of physical transformations. A list of reasonable physical requirements on the algebraic structure is given. We also consider the existence and structure of indefinite inner product representations and obtain various results for obtaining an indefinite inner product representation.


Left Ideal Product Representation Class Constraint Cyclic Vector Degenerate System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Grundling, H. B. G. S., Hurst, C. A.: Algebraic quantisation of systems with a gauge degeneracy. Commun. Math. Phys. 98, 369–390 (1985).Google Scholar
  2. 2.
    Dirac, P. A. M.: Lectures in quantum mechanics. New York: Belfer Graduate School of Science, Yeshiva University, 1964.Google Scholar
  3. 3.
    Segal, I. E.: Mathematical problems of relativistic physics. Providence, R. I.: American Mathematical Society, 1963.Google Scholar
  4. 4.
    Strocchi, F., Wightman, A. S.: Proof of the charge superselection rule in local relativistic quantum field theory. J. Math. Phys. 15, 2198–2224 (1974).Google Scholar
  5. 5.
    Grundling, Hendrik, Hurst, C. A.: Algebraic structures of degenerate systems, physical requirements and the indefinite metric. 1986 ( Submitted for publication).Google Scholar
  6. 6.
    Gupta, S. N.: Theory of longitudinal photons in quantum electrodynamics. Proc. Phys. Soc. London A63, 681–691 (1950).Google Scholar
  7. Bleuler, K.: Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen. Hely. Phys. Acta 23, 567–586 (1950).Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Hendrik Grundling
    • 1
  • C. A. Hurst
    • 1
  1. 1.University of AdelaideAustralia

Personalised recommendations