Singular cotangent bundle reduction & spin Calogero–Moser systems
نویسندگان
چکیده
منابع مشابه
O ct 2 00 8 SINGULAR COTANGENT BUNDLE REDUCTION & SPIN CALOGERO - MOSER SYSTEMS
We develop a bundle picture for singular symplectic quotients of cotangent bundles acted upon by cotangent lifted actions for the case that the configuration manifold is of single orbit type. Furthermore, we give a formula for the reduced symplectic form in this setting. As an application of this bundle picture we consider Calogero-Moser systems with spin associated to polar representations of ...
متن کامل2 00 4 Singular Cotangent Bundle Reduction & Spin Calogero - Moser Systems
We develop a bundle picture for the case that the configuration manifold has only a single isotropy type, and give a formula for the reduced symplectic form in this setting. Furthermore, as an application of this bundle picture we consider Calogero-Moser systems with spin associated to polar representations of compact Lie groups.
متن کاملDirac Cotangent Bundle Reduction
The authors’ recent paper in Reports in Mathematical Physics develops Dirac reduction for cotangent bundles of Lie groups, which is called Lie– Dirac reduction. This procedure simultaneously includes Lagrangian, Hamiltonian, and a variational view of reduction. The goal of the present paper is to generalize Lie–Dirac reduction to the case of a general configuration manifold; we refer to this as...
متن کاملThe Orbit Bundle Picture of Cotangent Bundle Reduction
Cotangent bundle reduction theory is a basic and well developed subject in which one performs symplectic reduction on cotangent bundles. One starts with a (free and proper) action of a Lie group G on a configuration manifold Q, considers its natural cotangent lift to T ∗Q and then one seeks realizations of the corresponding symplectic or Poisson reduced space. We further develop this theory by ...
متن کاملSingular Poisson Reduction of Cotangent Bundles
We consider the Poisson reduced space (T Q)/K with respect to a cotangent lifted action. It is assumed that K is a compact Lie group which acts by isometries on the Riemannian manifold Q and that the action on Q is of single isotropy type. Realizing (T ∗Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for p...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2008
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2007.11.008