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Quantum Knots and Quantum Braids
by
Samuel J. Lomonaco
UMBC
Coauthors: Louis H. Kauffman
In this talk, we show how to reconstruct knot theory in such a way that it s intimately related to quantum physics. In particular, we give a blueprint for creating a quantum system that has the dynamic behavior of a closed knotted piece of rope moving in 3-space. Within this framework, knot invariants become physically measurable quantum observables, knot moves become unitary transformations, with knot dynamics determined by SchroedingerÂ’s equation. The same approach can also be applied to the theory of braids.
Toward the end of the talk, we briefly look at possible applications to superfluid vortices and to topological quantum computing in optical lattices.
Date received: March 6, 2012
Copyright © 2012 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbek-09.