The Index of discontinuous Vector Fields: Topological Particles and Vector Fields

Details The Index of discontinuous Vector Fields: Topological Particles and Vector Fields The Index of discontinuous Vector Fields: Topological Particles and Vector Fields

1992-02-26

arxiv.org/abs/hep-th/9202088v1

Physics

High Energy Physics

High Energy Physics - Theory

25 page

Scientific paper

We define the concepts of topological particles and topological radiation. These are nothing more than connected components of defects of a vector field. To each topological particle we assign an index which is an integer which is conserved under interactions with other particles much as electric charge is conserved. For space-like vector fields of space-times this index is invariant under all coordinate transformations. We propose the following physical principal: For physical vector fields the index changes only when there is radiation. As an implication of this principal we predict that any physical psuedo-vector field has index zero. The definition of the index is quite elementary. It only depends upon the concepts of continuity, compactness, the Euler-Poincare number, and the idea of inward pointing. The proof that this definition is well defined takes up most of the paper. The paper concludes with a list of properties of the index.

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