Lagrangian formulation, generalizations and quantization of null Maxwell's knots

Abstract

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.

24 pages, no figures

References in corpus (4)

• Knotted solutions, from electromagnetism to fluid dynamics
• More on Heisenberg's model for high energy nucleon-nucleon scattering
• Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics
• DBI scalar field theory for QGP hydrodynamics

Cited by in corpus (2)

• Finsler Geometries from Topological Electromagnetism
• Gravitoelectromagnetic knot fields