1992/02/26 by Daniel Henry Gottlieb, Daniel H. Gottlieb, Gottlieb, Daniel H. +2
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Commutative Algebra and Its Applications #Polynomial and algebraic computation #hep-th #math.GT
paper · pdf · doi:10.48550/arxiv.hep-th/9202088
25 page
arxiv created 1992/02/26 · arxiv updated 2009/11/30
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.