Hamiltonian reduction of unconstrained and constrained systems

Фаддеев, Людвиг Дмитриевич; Jackiw, R.

doi:10.1103/physrevlett.60.1692

Cited by 748 publications

(990 citation statements)

References 7 publications

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“…as can be seen from the first order BF term in the master lagrangian (see [13]). ψ, θ i and θ generate the gauge transformations for A i , B ij , C i and π i C .…”

Section: Maxwell Theorymentioning

confidence: 92%

Geometric approach to a massivepform duality

2003

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Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2 + 1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.

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“…as can be seen from the first order BF term in the master lagrangian (see [13]). ψ, θ i and θ generate the gauge transformations for A i , B ij , C i and π i C .…”

Section: Maxwell Theorymentioning

confidence: 92%

Geometric approach to a massivepform duality

2003

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“…Besides, one ought to mention the work [14] where it was proposed an alternative (to the Dirac procedure) way of reducing the equations of motion for theories with actions of the form S = ϕ A (η)η A − V (η) dt . One can verify that, in fact, the procedure of that work, in a part (the procedure does not reveal the gauge identities), is similar to our reduction procedure in the case of the first order equations (see Sect.…”

Section: Discussionmentioning

confidence: 99%

Canonical form of Euler–Lagrange equations and gauge symmetries

Geyer

Гитман

Tyutin

2003

J. Phys. A: Math. Gen.

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The structure of the Euler-Lagrange equations for a general Lagrangian theory (e.g. singular, with higher derivatives) is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to highest-order derivatives of nongauge coordinates, whereas gauge coordinates and their derivatives enter in the right hand sides of the equations as arbitrary functions of time. The reduction procedure reveals constraints in the Lagrangian formulation of singular systems and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the EulerLagrange equations. Thus, a constructive way of finding all the gauge generators within the Lagrangian formulation is presented. At the same time, it is proven that for local theories all the gauge generators are local in time operators.

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“…In the first one we compute the symplectic form in terms of the modes. This is straightforward, since the action is first order in time derivatives and it is well-known how to proceed in these cases [28] [29]. The resulting symplectic form will be non-singular, so it has an inverse.…”

Section: Quantizationmentioning

confidence: 99%

Quantization of the open string on plane-wave limits of and non-commutativity outside branes

Horcajada

Ruiz

2008

Nuclear Physics B

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The open string on the plane-wave limit of dS n × S n with constant B 2 and dilaton background fields is canonically quantized. This entails solving the classical equations of motion for the string, computing the symplectic form, and defining from its inverse the canonical commutation relations. Canonical quantization is proved to be perfectly suited for this task, since the symplectic form is unambiguously defined and non-singular. The string position and the string momentum operators are shown to satisfy equal-time canonical commutation relations. Noticeably the string position operators define non-commutative spaces for all values of the string worldsheet parameter σ, thus extending non-commutativity outside the branes on which the string endpoints may be assumed to move. The Minkowski spacetime limit is smooth and reproduces the results in the literature, in particular non-commutativity gets confined to the endpoints.

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Hamiltonian reduction of unconstrained and constrained systems

Cited by 748 publications

References 7 publications

Geometric approach to a massivepform duality

Geometric approach to a massivepform duality

Canonical form of Euler–Lagrange equations and gauge symmetries

Quantization of the open string on plane-wave limits of and non-commutativity outside branes

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