Mathematics

Prof. Louis H. Kauffman
University of Illinois at Chicago

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.