Hamiltonian analysis of ModMax nonlinear electrodynamics in the first order formalism

Abstract

In this work we study the so-called ModMax nonlinear electrodynamics, which is a novel model designed to preserve duality rotations and conformal transformations, such as the Maxwell's equations do. This model allows to study diverse gravitational phenomena when is coupled to General Relativity, in particular charged black holes and gravitational waves. In the present work we focus in the dynamics and Hamiltonian analysis of the model. Specifically, we analyze the propagation of the discontinuities of the field and obtain the corresponding dispersion relations. To perform the Hamiltonian analysis we adopt the first order formalism develop by Plebański and follow the Dirac method for theories with constraints. We derive the effective Hamiltonian, classify all the constraints and identify the degrees of freedom. We prove that the effective Hamiltonian is strictly bounded from below and investigate the existence of non trivial minima.

10 Pages, No Figures, Accepted to publication in IJMP A

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• Higher-dimensional black holes with a conformally invariant Maxwell source
• Asymptotic charged BTZ black hole solutions
• Black holes and gravitational waves sourced by non-linear duality rotation-invariant conformal electromagnetic matter
• Nonlinear arcsin-electrodynamics
• Inflation-Produced Magnetic Fields in Nonlinear Electrodynamics
• Black-hole solution in nonlinear electrodynamics with the maximum allowable symmetries
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Cited by in corpus (7)

• Shadow, lensing, quasinormal modes, greybody bounds and neutrino propagation by dyonic ModMax black holes
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Maximally symmetric nonlinear extension of electrodynamics and charged particles
• Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
• Flows in the Space of Interacting Chiral Boson Theories
• Thermal and Optical Signatures of Einstein-Dyonic ModMax Black Holes with GUP and Plasma Modifications
• Stable Magnetic Lorentz-Violating Vacua in Gauge-Invariant Nonlinear Electrodynamics