Search results for "Cotangent bundle"

showing 4 items of 4 documents

Covariant phase space quantization of the Jackiw-Teitelboim model of two-dimensional gravity

1992

Abstract On the basis of the covariant phase space formulation of field theory we analyze the Jackiw-Teitelboim model of two-dimensional gravity on a cylinder. We compute explicitly the symplectic structure showing that the (reduced) phase space is the cotangent bundle of the space of conjugacy classes of the PSL(2, R ) group. This makes it possible to quantize the theory exactly. The Hilbert space is given by the character functions of the PSL (2, R ) group. As a byproduct, this implies the complete equivalence with the PSL (2, R )-topological gravity model.

PhysicsNuclear and High Energy PhysicsHilbert spaceCotangent spaceSpace (mathematics)symbols.namesakeConjugacy classPhase spaceQuantum mechanicssymbolsCotangent bundlePhase space formulationCovariant transformationMathematical physicsPhysics Letters B
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Numerical Kodaira Dimension

2014

In this chapter we study, following [30] , the first properties of the Zariski decomposition of the cotangent bundle of a nonrational foliation. In particular, we shall give a detailed description of the negative part of that Zariski decomposition, and we shall obtain a detailed classification of foliations whose Zariski decomposition is reduced to its negative part (i.e. foliations of numerical Kodaira dimension 0). We shall also discuss the “singular” point of view adopted in [30].

Pure mathematicsMathematics::Algebraic GeometryFoliation (geology)Decomposition (computer science)Cotangent bundleKodaira dimensionPoint (geometry)Mathematics::Symplectic GeometryMathematics
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The Rationality Criterion

2014

In this chapter we explain a remarkable theorem of Miyaoka [32] which asserts that a foliation whose cotangent bundle is not pseudoeffective is a foliation by rational curves. The original Miyaoka’s proof can be thought as a foliated version of Mori’s technique of construction of rational curves by deformations of morphisms in positive characteristic [33].

Pure mathematicsMathematics::Dynamical SystemsMathematics::Algebraic GeometryMorphismAlgebraic surfaceFoliation (geology)Principle of rationalityCotangent bundleRationalityMathematics::Differential GeometryMathematics::Symplectic GeometryEcological rationalityMathematics
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Closed star products and cyclic cohomology

1992

We define the notion of a closed star product. A (generalized) star product (deformation of the associative product of functions on a symplectic manifold W) is closed iff integration over W is a trace on the deformed algebra. We show that for these products the cyclic cohomology replaces the Hochschild cohomology in usual star products. We then define the character of a closed star product as the cohomology class (in the cyclic bicomplex) of a well-defined cocycle, and show that, in the case of pseudodifferential operators (standard ordering on the cotangent bundle to a compact Riemannian manifold), the character is defined and given by the Todd class, while in general it fails to satisfy t…

Pure mathematicsStatistical and Nonlinear PhysicsMathematics::Algebraic TopologyCohomologyAlgebraMathematics::K-Theory and HomologyCup productDe Rham cohomologyCotangent bundleEquivariant cohomologyTodd classMathematics::Symplectic GeometryMathematical PhysicsSymplectic manifoldQuantum cohomologyMathematicsLetters in Mathematical Physics
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