Chern-Simons states of photons and gravitons

Abstract

We consider an alternative quantization of the electromagnetic field around the Chern-Simons state $\psi_{CS}$ which is a zero energy solution of quantum electrodynamics. The solution determines a stochastic process which is a random perturbation of the self-duality equation for the electromagnetic potential ${\bf A}$. The stochastic process defines a solution of the Schr\"odinger equation with the initial condition $\psi_{CS}\chi$ where $\chi({\bf A})$ is an analytic function of ${\bf A}$ decaying fast at large ${\bf A}$. The method can be applied to a quantization of non-Abelian gauge theories by means of a stochastic self-duality equation. A quantization of massless spin 2 tensor fields (based on self-duality) and its extension to a quantization of gravity are also discussed.