scholarly journals Coadjoint orbits of the Virasoro group

1988 ◽  
Vol 114 (1) ◽  
pp. 1-53 ◽  
Author(s):  
Edward Witten
Keyword(s):  
Coadjoint Orbits ◽  
Virasoro Group

scholarly journals GEODESIC FLOW ON EXTENDED BOTT–VIRASORO GROUP AND GENERALIZED TWO-COMPONENT PEAKON TYPE DUAL SYSTEMS

2008 ◽  
Vol 20 (10) ◽  
pp. 1191-1208 ◽  
Author(s):  
PARTHA GUHA
Keyword(s):  
Evolution Equations ◽  
Boussinesq System ◽  
Coadjoint Orbits ◽  
Dual Systems ◽  
Hamiltonian Flows ◽  
Lie Algebraic Structure ◽  
Two Component ◽  
Integrable Evolution ◽  
Virasoro Group ◽  
Systematic Derivation

This paper discusses an algorithmic way of constructing integrable evolution equations based on Lie algebraic structure. We derive, in a pedagogical style, a large class of two-component peakon type dual systems from their two-component soliton equations counter part. We study the essential aspects of Hamiltonian flows on coadjoint orbits of the centrally extended semidirect product group [Formula: see text] to give a systematic derivation of the dual counter parts of various two-component of integrable systems, viz., the dispersive water wave equation, the Kaup–Boussinesq system and the Broer–Kaup system, using moment of inertia operators method and the (frozen) Lie–Poisson structure. This paper essentially gives Lie algebraic explanation of Olver–Rosenau's paper [31].

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

scholarly journals Loop variables and the Virasoro group

1993 ◽  
Vol 405 (2-3) ◽  
pp. 367-388 ◽  
Author(s):  
B. Sathiapalan
Keyword(s):  
Virasoro Group

The Darboux coordinate system and Holstein–Primakoff representations on Kähler manifolds

2006 ◽  
Vol 84 (10) ◽  
pp. 891-904
Author(s):  
J R Schmidt
Keyword(s):  
Coordinate System ◽  
Lie Groups ◽  
Lie Algebra ◽  
Poisson Structure ◽  
Kähler Manifolds ◽  
Coadjoint Orbits ◽  
Kahler Manifolds ◽  
Canonical Transformations ◽  
Kahler Geometry

The Kahler geometry of minimal coadjoint orbits of classical Lie groups is exploited to construct Darboux coordinates, a symplectic two-form and a Lie–Poisson structure on the dual of the Lie algebra. Canonical transformations cast the generators of the dual into Dyson or Holstein–Primakoff representations.PACS Nos.: 02.20.Sv, 02.30.Ik, 02.40.Tt

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