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 $\mathbf{A}$. The stochastic process defines a solution of the Schrödinger equation with the initial condition ${\psi }_{CS}\chi$ where $\chi (\mathbf{A})$ is an analytic function of $\mathbf{A}$ decaying fast at large $\mathbf{A}$. 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.

21 pages, accepted in EPJplus