Communications in Mathematical Physics

, Volume 98, Issue 3, pp 369–390 | Cite as

Algebraic quantization of systems with a gauge degeneracy

  • Hendrik B. G. S. Grundling
  • C. A. Hurst


Systems with a gauge degeneracy are characterized either by supplementary conditions, or by a set of generators of gauge transformations, or by a set of constraints deriving from Dirac's canonical constraint method. These constraints can be expressed either as conditions on the field algebra ℱ, or on the states on ℱ. In aC*-algebra framework, we show that the state conditions give rise to a factor algebra of a subalgebra of the field algebra ℱ. This factor algebra, ℛ, is free of state conditions. In this formulation we show also that the algebraic conditions can be treated in the same way as the state conditions. The connection between states on ℱ and states on ℛ is investigated further within this framework, as is also the set of transformations which are compatible with the set of constraints. It is also shown that not every set of constraints can give rise to a nontrivial system. Finally as an example, the abstract theory is applied to the electromagnetic field, and this treatment can be generalized to all systems of bosons with linear constraints. The question of dynamics is not discussed.


Neural Network Complex System State Condition Electromagnetic Field Nonlinear Dynamics 
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-Verlag 1985

Authors and Affiliations

  • Hendrik B. G. S. Grundling
    • 1
  • C. A. Hurst
    • 1
  1. 1.Department of Mathematical PhysicsUniversity of Adelaide

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