Search results for "Symplectomorphism"

showing 4 items of 4 documents

Diffeomorphisms, Noether charges, and the canonical formalism in two-dimensional dilaton gravity

1995

We carry out a parallel study of the covariant phase space and the conservation laws of local symmetries in two-dimensional dilaton gravity. Our analysis is based on the fact that the Lagrangian can be brought to a form that vanishes on-shell giving rise to a well-defined covariant potential for the symplectic current. We explicitly compute the symplectic structure and its potential and show that the requirement to be finite and independent of the Cauchy surface restricts the asymptotic symmetries.

AstrofísicaPhysicsGravitacióSymplectic representationsymbols.namesakeSymplectic vector spaceCauchy surfaceClassical mechanicssymbolsDilatonNoether's theoremSymplectomorphismMathematics::Symplectic GeometrySymplectic geometryMathematical physicsSymplectic manifoldPhysical Review D
researchProduct

Supermanifolds, Symplectic Geometry and Curvature

2016

We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.

Pure mathematicsMathematical analysisSymplectic representationGeneral Relativity and Quantum CosmologyHigh Energy Physics::TheorySymplectic vector spaceMathematics::Differential GeometrySymplectomorphismMathematics::Symplectic GeometryMoment mapGeometry and topologyScalar curvatureSymplectic geometrySymplectic manifoldMathematics
researchProduct

On the geometry of the characteristic class of a star product on a symplectic manifold

2001

The characteristic class of a star product on a symplectic manifold appears as the class of a deformation of a given symplectic connection, as described by Fedosov. In contrast, one usually thinks of the characteristic class of a star product as the class of a deformation of the Poisson structure (as in Kontsevich's work). In this paper, we present, in the symplectic framework, a natural procedure for constructing a star product by directly quantizing a deformation of the symplectic structure. Basically, in Fedosov's recursive formula for the star product with zero characteristic class, we replace the symplectic structure by one of its formal deformations in the parameter $\hbar$. We then s…

Statistical and Nonlinear PhysicsGeometrySymplectic representationSymplectic matrixSymplectic vector spaceMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)SymplectomorphismMoment mapMathematics::Symplectic GeometryMathematical PhysicsSymplectic geometryQuantum cohomologySymplectic manifoldMathematics
researchProduct

Symplectic Applicability of Lagrangian Surfaces

2009

We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equa- tions. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.

Mathematics - Differential GeometryPure mathematicsdifferential invariantsSymplectic vector spaceFOS: MathematicsSymplectomorphismMoment mapMathematics::Symplectic GeometryMathematical PhysicsMathematicsSymplectic manifoldapplicabilityLagrangian surfaceslcsh:MathematicsMathematical analysisSymplectic representationmoving frameslcsh:QA1-939Symplectic matrixaffine symplectic geometryAffine geometry of curvesDifferential Geometry (math.DG)Lagrangian surfaces; affine symplectic geometry; moving frames; differential invariants; applicability.Geometry and TopologyAnalysisSymplectic geometry
researchProduct