Physics

Prof. R. Shankar
IMSc., Chennai

Abstract : 

The inner product is central to the physical interpretation of quantum

mechanics. It also induces a geometry in the space of physical states of a
quantum system. In the past few decades, these ideas have been applied to
characterize the phases of quantum condensed matter.

I will first review the concept of distances and geometric phases in quantum
systems, how it is applied to the system of electrons in a periodic potential
and it's physical manifestations therein. I will then show how it leads to
a nice visualisation of mean field states as surfaces in finite dimensional
spaces. Finally, I will discuss some of the issues involved in generalising 
these ideas to correlated states.