Central extensions and physics

Tuynman, Gijs M.; Wiegerinck, W.A.J.J.

doi:10.1016/0393-0440(87)90027-1

Cited by 51 publications

(49 citation statements)

References 9 publications

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“…e.g. [11]. For N=2 this is exactly the quantization condition (3.85) in our survey [6], which we imposed for quite different (self-adjointness) reasons, however.…”

Section: Introductionmentioning

confidence: 94%

Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. III. Sutherland Type Systems and their Duals

Ruijsenaars¹

1995

Publ. Res. Inst. Math. Sci.

240

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We present an explicit construction of an action-angle map for the nonrelativistic N-particle Sutherland system and for two different generalizations thereof, one of which may be viewed as a relativistic version. We use the map to obtain detailed information concerning dynamical issues such as oscillation periods and equilibria, and to obtain simple formulas for partition functions. The nonrelativistic and relativistic Sutherland systems give rise to dual integrable systems with a solitonic long-time asymptotics that is explicitly described. We show that the second generalization is self-dual, and that its reduced phase space can be densely embedded in P N~l with its standard Kahler form, yielding commuting global flows. In a certain limit the reduced action-angle map converges to the quotient of Fourier transformation on C^ under the standard projection

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“…e.g. [11]. For N=2 this is exactly the quantization condition (3.85) in our survey [6], which we imposed for quite different (self-adjointness) reasons, however.…”

Section: Introductionmentioning

confidence: 94%

Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. III. Sutherland Type Systems and their Duals

Ruijsenaars¹

1995

Publ. Res. Inst. Math. Sci.

240

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“…[TW87] and [Bry93] for the infinite-dimensional case). Based on these observations, Tuynman and Wiegerinck gave a proof of the exactness of (1) in Hj (g, R) for finite-dimensional Lie If G is smoothly paracompact, it can be obtained quite directly from the de Rham Theorem, but in general one has to construct it directly.…”

mentioning

confidence: 99%

Central extensions of infinite-dimensional Lie groups

Neeb¹

2002

Annales De L’institut Fourier

123

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“…If this projection is interpreted as coming from the projection (60) off e L~(H3) to/_~(R2), it is evident that the projection of '0 to tp ~ is only possible due to the compactness of the central group T. This fact has also been observed in prequantization (Tuynman and Wiegerinck, 1987). The trace (66) is of Haar type, since it satisfies the axiom (49b), for example, as follows: using the formulas for tp ~ o, and *, we obtain from the left-hand side…”

Section: (Eio(x-lq;y)) : Eio(xq;-y)mentioning

confidence: 80%

“…As is well known, the second cohomology space H2(R 2, R/2~r) of cocycles from R 2 to R (mod 2"rr) is not trivial (Tuynman and Wiegerinck, 1987). Since 2-cocycleS classify central extensions, inequivalent 2-cocycles give rise to inequivalent central extensions.…”

Section: Tile Heisenberg Groupmentioning

confidence: 98%

Projective fourier duality and Weyl quantization

Aldrovandi

Saeger

1997

Int J Theor Phys

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The Weyl-Wigner correspondence prescription, which makes great use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. Both an Abelian and a symmetric projective Kac algebra are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyi formula arises naturally as an irreducible component of the duality mapping between these projective algebras.

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Central extensions and physics

Cited by 51 publications

References 9 publications

Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. III. Sutherland Type Systems and their Duals

Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. III. Sutherland Type Systems and their Duals

Central extensions of infinite-dimensional Lie groups

Projective fourier duality and Weyl quantization

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