Generalized Reduction Procedure: Symplectic and Poisson Formalism
نویسندگان
چکیده
منابع مشابه
Generalized Reduction Procedure: Symplectic and Poisson Formalism
We present a generalized reduction procedure which encompasses the one based on the momentum map and the projection method. By using the duality between manifolds and ring of functions defined on them, we have cast our procedure in an algebraic context. In this framework we give a simple example of reduction in the non-commutative setting. Partially supported by the Italian Consiglio Nazionale ...
متن کاملTriangular Poisson Structures on Lie Groups and Symplectic Reduction
We show that each triangular Poisson Lie group can be decomposed into Poisson submanifolds each of which is a quotient of a symplectic manifold. The Marsden–Weinstein–Meyer symplectic reduction technique is then used to give a complete description of the symplectic foliation of all triangular Poisson structures on Lie groups. The results are illustrated in detail for the generalized Jordanian P...
متن کاملDimensional Reduction for Generalized Poisson Brackets
We discuss dimensional reduction for Hamiltonian systems which possess nonconstant Poisson brackets between pairs of coordinates and between pairs of momenta. The associated Jacobi identities imply that the dimensionally reduced brackets are always constant. Some examples are given alongside the general theory.
متن کاملSymplectic Groupoids and Poisson Manifolds
0. Introduction. A symplectic groupoid is a manifold T with a partially defined multiplication (satisfying certain axioms) and a compatible symplectic structure. The identity elements in T turn out to form a Poisson manifold To? and the correspondence between symplectic groupoids and Poisson manifolds is a natural extension of the one between Lie groups and Lie algebras. As with Lie groups, und...
متن کاملGeneralized Classical Brst Cohomology and Reduction of Poisson Manifolds
In this paper, we formulate a generalization of the classical BRST construction which applies to the case of the reduction of a poisson manifold by a submanifold. In the case of symplectic reduction, our procedure generalizes the usual classical BRST construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold, i.e. the case of reducible “first c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fortschritte der Physik/Progress of Physics
سال: 1994
ISSN: 0015-8209,1521-3979
DOI: 10.1002/prop.2190420502