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Lagrangian formulation, generalizations and quantization of null Maxwell's knots
preprintposted on 2023-11-30, 05:20 authored by Horatiu Nastase, Jacob Sonnenschein
Knotted solutions to electromagnetism are investigated as an independent subsector of the theory. We write down a Lagrangian and a Hamiltonian formulation of Bateman's construction for the knotted electromagnetic solutions. We introduce a general definition of the null condition and generalize the construction of Maxwell's theory to massless free complex scalar, its dual two form field, and to a massless DBI scalar. We set up the framework for quantizing the theory both in a path integral approach, as well as the canonical Dirac method for a constrained system. We make several observations about the semi-classical quantization of systems of null configurations.