Semiclassical approximation and noncommutative geometry

Semiclassical approximation and noncommutative geometry

We consider the long time semiclassical evolution for the linear Schrödinger equation. We show that, in the case of chaotic underlying classical dynamics and for times up to ~, ǫ > 0, the symbol of a propagated observable by the corresponding von Neumann-Heisenberg equation is, in a sense made precise below, precisely obtained by the push-forward of the symbol of the observable at time t = 0. T...

SEMICLASSICAL ANYON DYNAMICS IN MATTER AND NONCOMMUTATIVE GEOMETRY: A BERRY PHASE CONNECTION S.Dhar

An explicit connection has been provided between the semi-classical dynamics of anyon excitations in Ga-As alloys and the motion of a 2 + 1-dimensional spinning particle (or anyon) in electromagnetic field in the Non-Commutative (NC) geometry framework. The Berry curvatures play a major role in the analysis. It is also established that the bulk parameters of the former can be mapped to the poin...

Noncommutative geometry

Noncommutative Geometry and Quantization

The purpose of these lectures is to survey several aspects of noncommutative geometry, with emphasis on its applicability to particle physics and quantum field theory. By now, it is a commonplace statement that spacetime at short length —or high energy— scales is not the Cartesian continuum of macroscopic experience, and that older methods of working with functions on manifolds must be rethough...

Noncommutative geometry and reality

We introduce the notion of real structure in our spectral geometry. This notion is motivated by Atiyah’s KR-theory and by Tomita’s involution J. It allows us to remove two unpleasant features of the “Connes-Lott” description of the standard model, namely, the use of bivector potentials and the asymmetry in the Poincare duality and in the unimodularity condition.