The Egorov theorem for transverse Dirac-type operators on foliated manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:57

Article

Kordyukov, Yuri A.

关键词: noncommutative geometry;    pseudodifferential operators;    riemannian foliations;    geodesic flow;    transversally elliptic operators;    Dirac operator;   

DOI  :  10.1016/j.geomphys.2007.08.002

来源: Elsevier

【 摘 要 】

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. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free