Lagrangian Formulation, Generalizations and Quantization of Null Maxwell's Knots

Horatiu Nastase, Jacob Sonnenschein

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number1800042
JournalFortschritte der Physik
Issue number8-9
StatePublished - 1 Aug 2018


  • Lagrangian formulation
  • knotted Maxwell solutions


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