Causal Self-Dual Electrodynamics

Causal Self-Dual Electrodynamics

18 May 2024 | Jorge G. Russo and Paul K. Townsend
The paper discusses the properties of nonlinear electrodynamics (NLED) theories, focusing on their causal behavior in both weak and strong fields. The authors show that any NLED theory that is causal for weak fields but acausal for strong fields can be transformed into a unique causal and self-dual (electromagnetic duality invariant) theory with the same Lagrangian at zero magnetic field. This transformation is achieved by constructing a general causal self-dual NLED, which demonstrates that strong-field causality is implied by weak-field causality for self-dual theories. The paper provides explicit examples to illustrate these results, including the modified Maxwell (ModMax) theory and its extensions. The authors also derive the necessary conditions for a Lagrangian density to define a causal NLED, emphasizing the importance of convexity conditions and the strong-field causality condition. They conclude by presenting a general form of the Lagrangian density for causal self-dual NLED and discuss the implications for future research, including the potential inclusion of gravity.The paper discusses the properties of nonlinear electrodynamics (NLED) theories, focusing on their causal behavior in both weak and strong fields. The authors show that any NLED theory that is causal for weak fields but acausal for strong fields can be transformed into a unique causal and self-dual (electromagnetic duality invariant) theory with the same Lagrangian at zero magnetic field. This transformation is achieved by constructing a general causal self-dual NLED, which demonstrates that strong-field causality is implied by weak-field causality for self-dual theories. The paper provides explicit examples to illustrate these results, including the modified Maxwell (ModMax) theory and its extensions. The authors also derive the necessary conditions for a Lagrangian density to define a causal NLED, emphasizing the importance of convexity conditions and the strong-field causality condition. They conclude by presenting a general form of the Lagrangian density for causal self-dual NLED and discuss the implications for future research, including the potential inclusion of gravity.
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