Causal self-dual nonlinear electrodynamics from the Born-Infeld theory
TLDR
A new auxiliary-field formulation for self-dual nonlinear electrodynamics, based on Born-Infeld theory, yields causal models and general solutions.
Key contributions
- Introduces an auxiliary-field formulation for self-dual nonlinear electrodynamics (NLED).
- Shows NLED models derived from Born-Infeld theory are causal.
- Provides a general solution for the self-duality equation.
- Relates the new formulation to the Russo and Townsend approach.
Why it matters
This paper advances self-dual nonlinear electrodynamics by presenting a new, causal formulation based on Born-Infeld theory. It provides a general solution to the self-duality equation, crucial for theoretical physics. This work also connects different theoretical approaches, enhancing field coherence.
Original Abstract
Recently we have proposed a new auxiliary-field formulation for self-dual nonlinear electrodynamics (NLED) which makes use of two building blocks: (i) a seed self-dual theory $L(F_{μν};g)$, where $F_{μν}$ is the electromagnetic field strength and $g$ a duality-invariant coupling constant; and (ii) a scalar potential $W(ψ)$. Our formulation is based on the Lagrangian $ \mathfrak{L}(F_{μν};ψ) = L(F_{μν};ψ) + W(ψ)$, where $ψ$ is an auxiliary scalar field. Integrating out $ψ$, using its equation of motion, one obtains a $\mathsf{U}(1)$ duality-invariant NLED. Different self-dual NLEDs are derived by choosing different potentials $W(ψ)$. In the case that the seed Lagrangian defines the Born-Infeld theory, in this paper we demonstrate that the resulting models for self-dual NLED are causal and provide a general solution of the self-duality equation. We also elaborate on the procedure to relate our formulation to that developed by Russo and Townsend.
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