Every symplectic manifold is a (linear) coadjoint orbit
نویسندگان
چکیده
منابع مشابه
Minimal coadjoint orbits and symplectic induction
Let (X,ω) be an integral symplectic manifold and let (L,∇) be a quantum line bundle, with connection, over X having ω as curvature. With this data one can define an induced symplectic manifold (X̃, ω X̃ ) where dim X̃ = 2 + dimX . It is then shown that prequantization on X becomes classical Poisson bracket on X̃ . We consider the possibility that if X is the coadjoint orbit of a Lie group K then X̃ ...
متن کاملBRST quantization and coadjoint orbit theories.
A new ‘harmonic’ BRST method is presented for quantizing those dynamical systems having second-class constraints which split into holomorphic and antiholomorphic algebras. These theories include those whose phase spaces are coadjoint orbits of a compact semisimple Lie group. The method also applies to theories with holomorphic first-class constraints which have nonvanishing brackets with their ...
متن کاملThe Symplectic Normal Space of a Cotangent-lifted Action
For the cotangent bundle T Q of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the direct sum of the cotangent bundle of a linear space and a symplectic linear space coming from reduction of a coadjoint orbit. This characterization of the s...
متن کاملWick quantisation of a symplectic manifold
The notion of the Wick star-product is covariantly introduced for a general symplectic manifold equipped with two transverse polarisations. Along the lines of Fedosov method, the explicit procedure is given to construct the Wick symbols on the manifold. The cohomological obstruction is identified to the equivalence between the Wick star-product and the Fedosov one. In particular in the Kähler c...
متن کاملSymmetry of a Symplectic Toric Manifold
The action of a torus group T on a symplectic toric manifold (M, ω) often extends to an effective action of a (nonabelian) compact Lie group G. We may think of T and G as compact Lie subgroups of the symplectomorphism group Symp(M, ω) of (M, ω). On the other hand, (M, ω) is determined by the associated moment polytope P by the result of Delzant [4]. Therefore, the group G should be estimated in...
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: Canadian Mathematical Bulletin
سال: 2021
ISSN: 0008-4395,1496-4287
DOI: 10.4153/s000843952100031x