Gauge Symmetries and Dirac Conjecture

Wang, Yong-Long; Li, Ziping; Wang, Ke

doi:10.1007/s10773-009-9961-9

Cited by 8 publications

(14 citation statements)

References 37 publications

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“…This is consistent with the claim made in Ref. 26, even when the calculations are wrong there. As a matter of fact this example shows that, even getting different gauge transformation laws in both treatments, the direct application of the original theory gives the right physical information and reinforce the fundamental character of the construction.…”

Section: Hamiltonian Analysissupporting

confidence: 93%

“…1 )) and using the results 1 and 2 of Section III (N 1 = e, N (p) 1 = g) 1 2 Rank Ω | φ ′ s = N − 1 2 (l + g + e), which of course coincides with (26). Thus the geometrical meaning of g + e is the number of null vectors of Ω | φ ′ s .…”

Section: Formalism Viewpointmentioning

confidence: 63%

“…Finally, we have 2 independent Lagrangian constraints (l = l 0 + l 1 + l 2 = 1 + 1 + 0 = 2), 1 gauge identity (g = g 0 + g 1 + g 2 = 0 + 0 + 1 = 1) and e = 3 effective parameters. Using expression (26), the number of physical degrees of freedom is…”

Section: An Example Involving a High Order Gauge Transformationmentioning

confidence: 99%

“…One of the main statements used in the proof of the formula for the physical degree of freedom count (26) was that Lagrangian and Hamiltonian gauge transformations should be equivalents in the total formalism. However it is well known this is not true in counterexamples to Dirac's conjecture and it is natural to ask if there are any changes to (26)? Let us study a particular example defined by the Lagrangian…”

Section: Appendix C: a Counterexample To Dirac's Conjecturementioning

confidence: 99%

“…In summary, we have 2 original variables (x and y), l = l 0 + l 1 = 1 + 0 = 1 independent Lagrangian constraints, g = g 0 + g 1 = 0 + 1 = 1 gauge identity and e = 2 effective gauge parameters (ε andε). Using the expression (26), the number of physical degrees of freedom is 2 − 1 2 (1 + 1 + 2) = 0,…”

Section: Hamiltonian Analysismentioning

confidence: 99%

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Lagrangian approach to the physical degree of freedom count

Díaz

Higuita

Montesinos

2014

Journal of Mathematical Physics

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In this paper we present a Lagrangian method that allows the physical degree of freedom count for any Lagrangian system without having to perform neither Dirac nor covariant canonical analyses. The essence of our method is to establish a map between the relevant Lagrangian parameters of the current approach and the Hamiltonian parameters that enter in the formula for the counting of the physical degrees of freedom as is given in Dirac's method. Once the map is obtained, the usual Hamiltonian formula for the counting can be expressed in terms of Lagrangian parameters only and therefore we can remain in the Lagrangian side without having to go to the Hamiltonian one. Using the map it is also possible to count the number of first and second-class constraints within the Lagrangian formalism only. For the sake of completeness, the geometric structure underlying the current approach--developed for systems with a finite number of degrees of freedom--is uncovered with the help of the covariant canonical formalism. Finally, the method is illustrated in several examples, including the relativistic free particle.Comment: LaTeX file, no figure

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Section: Hamiltonian Analysissupporting

confidence: 93%

Section: Formalism Viewpointmentioning

confidence: 63%

Section: An Example Involving a High Order Gauge Transformationmentioning

confidence: 99%

Section: Appendix C: a Counterexample To Dirac's Conjecturementioning

confidence: 99%

Section: Hamiltonian Analysismentioning

confidence: 99%

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Lagrangian approach to the physical degree of freedom count

Díaz

Higuita

Montesinos

2014

Journal of Mathematical Physics

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The Limit of Noether Conserved Charges is the Number of Primary First-Class Constraints in a Constrained System

Wang¹,

Zhao-Xia²,

Pan³

et al. 2012

Commun. Theor. Phys.

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We discuss the stationarity of generator G for gauge symmetries in two directions. One is to the motion equations defined by total Hamiltonian HT , and gives that the number of the independent coefficients in the generator G is not greater than the number of the primary first-class constraints, and the number of Noether conserved charges is not greater than that of the primary first-class constraints, too. The other is to the variances of canonical variables deduced from the generator G, and gives the variances of Lagrangian multipliers contained in extended Hamiltonian HE. And a second-class constraint generated by a first-class constraint may imply a new first-class constraint which can be combined by introducing other second-class constraints. Finally, we supply two examples. One with three first-class constraints (two is primary and one is secondary) has two Noether conserved charges, and the secondary first-class constraint is combined by three second-class constraints which are a secondary and two primary second-class constraints. The other with two first-class constraints (one is primary and one is secondary) has one Noehter conserved charge.

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