https://doi.org/10.1140/epjp/s13360-025-06193-4
Regular Article
Chern–simons states of photons and gravitons
Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50-204, Wroclaw, Poland
Received:
13
January
2025
Accepted:
6
March
2025
Published online:
3
April
2025
We consider an alternative quantization of the electromagnetic field around the Chern–Simons state 
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 
. The stochastic process defines a solution of the Schrödinger equation with the initial condition 
where 
is an analytic function of decaying fast at large . 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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
