Hamiltonian analysis of ModMax nonlinear electrodynamics in the first order formalism

TL;DR

This paper performs a Hamiltonian analysis of ModMax nonlinear electrodynamics, exploring its dynamics, constraints, and stability, with implications for gravitational phenomena such as black holes and gravitational waves.

Contribution

It provides the first Hamiltonian formulation of ModMax electrodynamics using the first order formalism and Dirac method, identifying constraints and degrees of freedom.

Findings

Effective Hamiltonian is bounded from below.

Constraints and degrees of freedom are classified.

Potential non-trivial minima are investigated.

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 Pleba\'nski 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.