UM Math Graduate Students Seminar

Armando Cabrera
University of Miami

will present

The Zeeman Topology on the Minkowski Spacetime

Friday, September 14, 2012, 3:45pm
Ungar Building Room 402


Abstract:The Minkowski Spacetime, which is R^4 eqquiped with a metric of signature 1, is the model of the Special Relativity. In this space we can define a partial order relation, x<y, when y is in the chronological future of x. It was proven by E.C. Zeeman that this relation is preserved by causal automorphisms (i.e., orthochronus Lorentz tranformations, translations and dilatations). However, as the usual topology on R^4 does not distinguish between timelike, lightlike and spacelike directions, it admits continuous functions that have no clear physical meaning, i.e., the previous relation is not preserved. In this talk we will define the Zeeman topology on the Minkowski Space and extract some important properties. This topology has the nice feature that the homeomorphisms are generated by Lorentz group, translations and dilatations; a brief description of the proof of this fact will be given.


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