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arXiv · 0708.1660

The Egorov theorem for transverse Dirac type operators on foliated manifolds

Yuri A. Kordyukov
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Abstract

Egorov's theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a first order transversally elliptic operator with the (classical) evolution of its symbols determined by the parallel transport along the orbits of the associated transverse bicharacteristic flow. For a particular case of a transverse Dirac operator, the transverse bicharacteristic flow is shown to be given by the transverse geodesic flow and the parallel transport by the parallel transport determined by the transverse Levi-Civita connection. These results allow us to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.

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BibTeXRIS

Yuri A. Kordyukov. 2007-08-13. The Egorov theorem for transverse Dirac type operators on foliated manifolds. https://doi.org/10.1016/j.geomphys.2007.08.002

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