Hamiltonian analysis of ModMax nonlinear electrodynamics in the first-order formalism

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 it is coupled to General Relativity, in particular charged black holes and gravitational waves. In this 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 Plebanski 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 nontrivial minima.

Automated summary

The study focuses on the dynamics and Hamiltonian analysis of the ModMax nonlinear electrodynamics model, particularly on analyzing the propagation of field discontinuities and deriving the effective Hamiltonian. The research proves the effective Hamiltonian is strictly bounded from below and investigates the existence of nontrivial minima.