Causal Self-Dual Electrodymanics

Causal Self-Dual Electrodymanics

18 May 2024 | Jorge G. Russo and Paul K. Townsend
This paper presents a study of causal self-dual electrodynamics, focusing on nonlinear electrodynamics (NLED) theories that are causal for weak fields but acausal for strong fields. It shows that for any such theory, there exists a unique causal and self-dual theory with the same Lagrangian at zero magnetic field. This is achieved through a construction that demonstrates that strong-field causality follows from weak-field causality for self-dual theories. NLED theories are generalizations of Maxwell electrodynamics, defined by a Lagrangian density function of the Lorentz scalars S and P, which are quadratic in the electric and magnetic fields. The conditions for a Lagrangian to define a causal NLED are derived, including convexity conditions and a strong-field causality condition. These conditions ensure that the theory is causal for both weak and strong fields. The paper discusses the implications of these conditions for various NLED theories, including Born's theory, Born-Infeld theory, and the Heisenberg-Euler theory. It shows that while many NLED theories are causal for weak fields, they may not be for strong fields. However, for self-dual theories, which are invariant under electromagnetic duality, the conditions ensure causality for both weak and strong fields. The paper also presents a method to convert non-self-dual NLED theories into self-dual ones that are causal. This is done by using a one-variable function ℓ(τ) derived from the Lagrangian density at zero magnetic field. The conditions for causality are then applied to this function, leading to a simple set of inequalities that ensure causality for self-dual NLED theories. The paper concludes with examples of self-dual NLED theories, including ModMax, ModMaxBorn, and logarithmic electrodynamics, and discusses the implications of these results for the study of nonlinear electrodynamics in various physical contexts. It also highlights the importance of causality in applications such as black hole physics and magnetars.This paper presents a study of causal self-dual electrodynamics, focusing on nonlinear electrodynamics (NLED) theories that are causal for weak fields but acausal for strong fields. It shows that for any such theory, there exists a unique causal and self-dual theory with the same Lagrangian at zero magnetic field. This is achieved through a construction that demonstrates that strong-field causality follows from weak-field causality for self-dual theories. NLED theories are generalizations of Maxwell electrodynamics, defined by a Lagrangian density function of the Lorentz scalars S and P, which are quadratic in the electric and magnetic fields. The conditions for a Lagrangian to define a causal NLED are derived, including convexity conditions and a strong-field causality condition. These conditions ensure that the theory is causal for both weak and strong fields. The paper discusses the implications of these conditions for various NLED theories, including Born's theory, Born-Infeld theory, and the Heisenberg-Euler theory. It shows that while many NLED theories are causal for weak fields, they may not be for strong fields. However, for self-dual theories, which are invariant under electromagnetic duality, the conditions ensure causality for both weak and strong fields. The paper also presents a method to convert non-self-dual NLED theories into self-dual ones that are causal. This is done by using a one-variable function ℓ(τ) derived from the Lagrangian density at zero magnetic field. The conditions for causality are then applied to this function, leading to a simple set of inequalities that ensure causality for self-dual NLED theories. The paper concludes with examples of self-dual NLED theories, including ModMax, ModMaxBorn, and logarithmic electrodynamics, and discusses the implications of these results for the study of nonlinear electrodynamics in various physical contexts. It also highlights the importance of causality in applications such as black hole physics and magnetars.
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