Geometry, Zitterbewegung, quantization

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...

Zitterbewegung Modeling

Guidelines for constructing point particle models of the electron with zitterbewegung and other features of the Dirac theory are discussed. Such models may at least be useful approximations to the Dirac theory, but the more exciting possibility is that this approach may lead to a more fundamental reality.

Zitterbewegung in Quantum Mechanics

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with qu...

Symplectic Geometry and Geometric Quantization 1

Hierarchical Shape-Adaptive Quantization for Geometry Compression

The compression of polygonal mesh geometry is still an active field of research as in 3d no theoretical bounds are known. This work proposes a geometry coding method based on predictive coding. Instead of using the vertex to vertex distance as distortion measurement, an approximation to the Hausdorffdistance is used resulting in additional degrees of freedom. These are exploited by a new adapti...