共查询到20条相似文献,搜索用时 15 毫秒
1.
Simone Gutt 《Letters in Mathematical Physics》2006,78(3):307-328
This note contains a short survey on some recent work on symplectic connections: properties and models for symplectic connections whose curvature is determined by the Ricci tensor, and a procedure to build examples of Ricci-flat connections. For a more extensive survey, see Bieliavsky et al. [Int. J. Geom. Methods Mod. Phys. 3, 375–420 2006]. This note also includes a moment map for the action of the group of symplectomorphisms on the space of symplectic connections, an algebraic construction of a large class of Ricci-flat symmetric symplectic spaces, and an example of global reduction in a non-symmetric case. 相似文献
2.
Pavol Ševera 《Letters in Mathematical Physics》2006,75(3):273-277
We introduce an affine-invariant version of generating functions of symplectic transformations of affine symplectic spaces,
together with a generalization for other symmetric symplectic spaces. The composition of these functions has a nice connection
with the Moyal product. 相似文献
3.
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein–Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require. 相似文献
4.
《Reports on Mathematical Physics》1999,43(1-2):35-42
We define a variational principle for symplectic connections of the Yang-Mills type. When the symplectic manifold is a compact surface we show that the moduli space of the connections which are extremals of the functional coincides with the Teichmüller space of the surface. We indicate that the noncompact situation is very different. 相似文献
5.
《Journal of Geometry and Physics》1999,30(3):233-265
We introduce a variational principle for symplectic connections and study the corresponding field equations. For two-dimensional compact symplectic manifolds we determine all solutions of the field equations. For two-dimensional non-compact simply connected symplectic manifolds we give an essentially exhaustive list of solutions of the field equations. Finally we indicate how to construct from solutions of the field equations on (M, ω) solutions of the field equations on the cotangent bundle to M with its standard symplectic structure. 相似文献
6.
Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two reduced conformal Poisson vector fields, again analogous to the dual pair construction for symplectic manifolds. Conformal Poisson systems form an interesting infinite-dimensional Lie algebra of foliate vector fields. Manifolds supporting such conformal vector fields include cotangent bundles, Lie–Poisson manifolds, and their natural quotients. 相似文献
7.
Sergei Khoroshkin Andrey Radul Vladimir Rubtsov 《Communications in Mathematical Physics》1993,152(2):299-315
We investigate the compatibility of symplectic Kirillov-Kostant-Souriau structure and Poisson-Lie structure on coadjoint orbits of semisimple Lie group. We prove that they are compatible for an orbit compact Lie group iff the orbit is hermitian symmetric space. We prove also the compatibility statement for non-compact hermitian symmetric space. As an example we describe a structure of symplectic leaves onCP
n
for this family. These leaves may be considered as a perturbation of Schubert cells. Possible applications to infinite-dimensional examples are discussed. 相似文献
8.
Jørgen Ellegaard Andersen Paolo Masulli Florian Schätz 《Communications in Mathematical Physics》2016,342(2):739-768
We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection, which was introduced by the first author. We establish a necessary and sufficient condition that guarantees the existence of a formal connection, and we describe the space of formal connections for a family as an affine space modelled on the formal symplectic vector fields. Moreover, we showthat if the parameter space has trivial first cohomology group, any two flat formal connections are related by an automorphism of the family of star products. 相似文献
9.
10.
This paper deals with moduli spaces of framed principal bundles with connections with irregular singularities over a compact Riemann surface. These spaces have been constructed by Boalch by means of an infinite-dimensional symplectic reduction. It is proved that the symplectic structure induced from the Atiyah–Bott form agrees with the one given in terms of hypercohomology. The main results of this paper adapt work of Krichever and of Hurtubise to give an interpretation of some Hitchin Hamiltonians as yielding Hamiltonian vector fields on moduli spaces of irregular connections that arise from differences of isomonodromic flows defined in two different ways. This relies on a realization of open sets in the moduli space of bundles as arising via Hecke modification of a fixed bundle. 相似文献
11.
Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters
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Denghui Li 《中国物理 B》2022,31(8):80202-080202
This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters. The boson-fermion correspondence for these symmetric functions have been presented. In virtue of quantum fields, we derive a series of infinite order nonlinear integrable equations, namely, universal character hierarchy, symplectic KP hierarchy and symplectic universal character hierarchy, respectively. In addition, the solutions of these integrable systems have been discussed. 相似文献
12.
《Journal of Geometry and Physics》2002,41(3):224-234
We construct and identify star representations canonically associated with holonomy-reducible simple symplectic symmetric spaces. This leads a non-commutative geometric realization of the correspondence between causal symmetric spaces of Cayley-type and Hermitian symmetric spaces of tube-type. 相似文献
13.
14.
Nai-Chung Conan Leung 《Communications in Mathematical Physics》1998,193(1):47-67
We study certain natural differential forms and their equivariant extensions on the space of connections. These forms are defined using the family local index theorem. When the
base manifold is symplectic, they define a family of symplectic forms on the space of connections. We will explain their relationships
with the Einstein metric and the stability of vector bundles. These forms also determine primary and secondary characteristic
forms (and their higher level generalizations).
Received: 27 February 1996 / Accepted: 7 July 1997 相似文献
15.
16.
《Physics letters. A》1998,247(3):191-197
We prove that symmetric decouplings of the exponential operator can be exploited to obtain symplectic integrators with arbitrary accuracy. 相似文献
17.
《Journal of Geometry and Physics》2006,56(10):1985-2009
Using Fedosov’s approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kähler–Poisson manifolds this construction provides, in particular, the formal symplectic groupoids with separation of variables. We show that the dual of a semisimple Lie algebra does not admit torsion-free Poisson contravariant connections. 相似文献
18.
Ambar N. Sengupta 《Journal of Geometry and Physics》2003,47(4):398-426
We prove that integration over the moduli space of flat connections can be obtained as a limit of integration with respect to the Yang–Mills measure defined in terms of the heat-kernel for the gauge group. In doing this we also give a rigorous proof of Witten’s formula for the symplectic volume of the moduli space of flat connections. Our proof uses an elementary identity connecting determinants of matrices along with a careful accounting of certain dense subsets of full measure in the moduli space. 相似文献
19.
Robin Forman 《Communications in Mathematical Physics》1993,151(1):39-52
By examining the lattice gauge approximation we show that the small volume limit of the 2-dimensional Yang-Mills functional integral is the natural symplectic measure on the moduli space of flat connections. 相似文献