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arXiv · 2503.04220

Chern-Simons states of photons and gravitons

Z. Haba
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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.

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Z. Haba. 2025-03-06. Chern-Simons states of photons and gravitons. https://arxiv.org/abs/2503.04220

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