Abstract:

What does a collection of interacting rigid tops have in common with the gauge theories that describe our fundamental theories of nature? The answer is: their Hilbert space! In this talk I will go over a basic exercise in quantum mechanics, which is finding the energies and eigenfunctions of a free rigid top. This alone is of interest in chemistry. Then we’ll see how this Hilbert space is the building block for an SU(2) gauge theory on a spatial lattice, namely the Hamiltonian formulation of Wilson’s lattice gauge theory. Once we’ve written this down, I’ll explain why the non-abelian form of Gauss’ law must be imposed “by hand”, and why this seems to be very difficult.

https://lbnl.zoom.us/j/98945893896?pwd=Q3BrUTBIajZ0SDJ1MXRGbWVHOE5Udz09