Louis H Kauffman
University of Illinois at Chicago, USA
Title: Braiding of Majorana fermions, topological quantum computation and the nature of Clifford algebras
Biography
Biography: Louis H Kauffman
Abstract
Majorana fermions are fermionic particles that are their own anti-particles. Mathematically, a standard fermion such as an electron can be seen as a composite of two Majorana fermions. At the level of operators in quantum field theory this is seen by writing F=a+ib where, F is the fermion annihilation operator and a and b are elements of a Clifford algebra where a^2= b^2=1 and ab=-ba. Then F*=a-ib and we have F^2=F*^2=0 and FF*+F*F is a scalar. Remarkably, rows of electrons in nanowires have been shown to have correlation behaviors that correspond to this decomposition and topologically remarkable is the fact that the underlying Majorana fermions have a natural braiding structure. This talk will discuss the braiding structure of Majorana fermions, possible applications to topological quantum computing and ways to understand the mathematical meaning of the fermion operators.