Algebraic quantization of systems with a gauge degeneracy

Grundling, Hendrik; Hurst, C. A.

doi:10.1007/bf01205789

Cited by 35 publications

(86 citation statements)

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“…In the present section we will summarize the algebric structures and the results of the papers by Grundling and Hurst [2,9,10,11,12] and by Manuceau et al [13,14] that are relevant for our examples. We refer to these papers for the proofs of the theorems and for further developments of the subject.…”

Section: Quantum Constraintsmentioning

confidence: 99%

“…We refer to these papers for the proofs of the theorems and for further developments of the subject. We will stay as close as possible to the notation of Grundling and Hurst in [2] and [11, Section 2].…”

Section: Quantum Constraintsmentioning

confidence: 99%

“…For this reason in the massless models certain factor spaces are needed ([1, Section B.2]) in order to construct the net of local algebras following the spirit of [1,Part A]. It is the intention of the present note to show that, before introducing the factor spaces, the bosonic massless models with helicity bigger than 0 fit completely into the general frame developed by Grundling and Hurst in [2] to treat systems with gauge degeneracy. We will make explicit the relation of the models with the general theory.…”

Section: Introductionmentioning

confidence: 99%

“…Since no field equations are explicitly used in the construction, the specification of the constraint set can not use heuristic arguments as in the example presented in [2,Section 5]. (But, at the same time, this last fact may be criticized, because we loose contact with Dirac's original theory of constraints [6].)…”

Section: Introductionmentioning

confidence: 99%

“…This function shows to be very useful to prove the covariance and the causality of the net and it also codes the degenerate character of the massless models with respect to the massive ones. It is the intention of the present note to point out that the massless bosonic examples with helicity bigger than 0 fit completely into the general theory that Grundling and Hurst [2] used to describe systems with gauge degeneracy.2 …”

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confidence: 99%

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Lledó¹

1997

Letters in Mathematical Physics

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Abstract. In [1, Part B] the authors describe a method for constructing directly (i.e. without using explicitly any field operator nor any concrete representation of the C * -algebra) nets of local C * -algebras associated to massless models with arbitrary helicity and that satisfy Haag-Kastler's axioms. In order to specify the sesquilinear-and the symplectic form of the CAR-and CCR-algebras, respectively, a certain operator-valued function β(·) is introduced. This function shows to be very useful to prove the covariance and the causality of the net and it also codes the degenerate character of the massless models with respect to the massive ones. It is the intention of the present note to point out that the massless bosonic examples with helicity bigger than 0 fit completely into the general theory that Grundling and Hurst [2] used to describe systems with gauge degeneracy.2

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Section: Quantum Constraintsmentioning

confidence: 99%

Section: Quantum Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Lledó¹

1997

Letters in Mathematical Physics

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Quantization of Constrained Systems

Klauder

2001

Methods of Quantization

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The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first-and second-class constraints from the point of view of coherent-state, phase-space path integration, and show that all such cases may be treated, within the original classical phase space, by using suitable path-integral measures for the Lagrange multipliers which ensure that the quantum system satisfies the appropriate quantum constraint conditions. Unlike conventional methods, our procedures involve no δ-functionals of the classical constraints, no need for dynamical gauge fixing of first-class constraints nor any average thereover, no need to eliminate second-class constraints, no potentially ambiguous determinants, as well as no need to add auxiliary dynamical variables expanding the phase space beyond its original classical formulation, including no ghosts. Besides several pedagogical examples, we also study: (i) the quantization procedure for reparameterization invariant models, (ii) systems for which the original set of Lagrange mutipliers are elevated to the status of dynamical variables and used to define an extended dynamical system which is completed with the addition of suitable conjugates and new sets of constraints and their associated Lagrange multipliers, (iii) special examples of alternative but equivalent formulations of given first-class constraints, as well as (iv) a comparison of both regular and irregular constraints. *

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Flat Non-Regular States on Weyl Algebras

Acerbi

1994

On Three Levels

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Algebraic quantization of systems with a gauge degeneracy

Cited by 35 publications

References 16 publications

Untitled

Untitled

Quantization of Constrained Systems

Flat Non-Regular States on Weyl Algebras

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