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Topological Models for Elementary Particles



Topological Dynamics in the Physical and Biological Sciences

The talk will be a survey of topological models for elementary particles including the work of Lord Kelvin, Herbert Jehle, Thomas Kephart, Jack Avrin, Sundance Bilson-Thompson and recent work of the speaker with Sundance Bilson-Thompson and Jonathan Hackett and work of the speaker on the Fibonacci model in quantum information theory. Lord Kelvin suggested that atoms (the elementary particles of his time) are knotted vortices in the luminiferous aether. Jehle (much later on) suggested that elemenary particles should be quantized knotted electromagnetic flux. Kephart and Buiny suggest that closed loops of gluon field can be knotted particles—knotted glueballs. Avrin notes that a three half-twisted Mobius band could be like a proton composed of three quarks mutually bound. Sundance Bilson-Thompson has a theory of framed three-braids that is a topological version of preons. In this theory we can think of particles as topological defects in networks of surfaces and some properties of embedded surfaces may sort out the matter. In the Fibonacci model for topological quantum computing, the system is generated by a braided anyonic abstract particle P that interacts with itself to produce itself (PP——-> P) or iteracts with itself to produce a neutral particle (PP———> 1). The elementary particle P of the Fibonacci model is a structure that can be seen as a logical particle, underlying all the mathematical structures that we know. Since this talk surveys such a range of ideas, it will be up to the speaker to find a way to summarize these diseparate views at the time of the talk.


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