Speaker
Prof.
Duco van Straten
Description
I will report on work in progress joint with Mauricio Garay from Paris.
Near a critical point of a Hamiltonian function on the symplectic $p-q$ plane, the level set $H(p,q)=c$ forms a simple closed loop that encloses an area and has the dimension of an action. In quantum theory the variables no longer commute: $pq-qp=h$. We introduce the notion of quantised area, which is a formal series in $h$. In examples we find strong integrality properties of the appearing coefficients that suggest looking for an enumerative meaning.