On the Trace Density in Deformation Quantization

doi:https://doi.org/10.1007/978-3-0348-9092-2_14

Book Chapter10.1007/978-3-0348-9092-2_14

On the Trace Density in Deformation Quantization

Boris Fedosov-1995-01-01-Birkhäuser Basel eBooks

15

TL;DRAbstract

Let Q: C ∞ (M)[[h]] → W D be a quantization map considered in the author’s papers [2, 3, 4]. Here M is a symplectic manifold of dimension 2n, W D the algebra of flat sections of the Weyl algebras bundle W with respect to an Abelian connection D on W. The coefficient bundle of W is supposed to be Hom(E,E) for some m-dimensional complex vector bundle E. The Abelian connection D depends thus on the symplectic connection ∂s on M and the connection ∂ E on E.

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Let Q: C ∞ (M)[[h]] → W D be a quantization map considered in the author’s papers [2, 3, 4]. Here M is a symplectic manifold of dimension 2n, W D the algebra of flat sections of the Weyl algebras bundle W with respect to an Abelian connection D on W. The coefficient bundle of W is supposed to be Hom(E,E) for some m-dimensional complex vector bundle E. The Abelian connection D depends thus on the symplectic connection ∂s on M and the connection ∂ E on E.

Keywords

Connection (principal bundle)Symplectic geometryAbelian groupMathematicsBundlePure mathematicsVector bundleTRACE (psycholinguistics)

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