XXV Workshop on Geometric Methods in Physics 2-8.07.2006

Aleksandr Komlov

A Grassmannian non-commutative U(1) sigma model and Bargmann-Fock space

We consider a Grassmanian version of the static non-commutative U(1) sigma model. It is defined by the quadratic energy functional $E(P)=||[a,P]||^2_{HS}$, where a:H\to H is the standard annihilation operator and P is an orthogonal projection in H. We use the Bargmann-Fock realization of H to describe all solutions P of rank 1 and to prove that the operator [a,P] is densely defined, when P is some BPS-solution of infinite rank and corank.