Proof of a Symmetrized Trace Conjecture for the Abelian Born-Infeld Lagrangian

Abstract

In this paper we prove a conjecture regarding the form of the Born-Infeld Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary fields. We show that the Lagrangian can be written as a symmetrized trace of Lorentz invariant bilinears in the field strength. More generally we prove a theorem regarding certain solutions of unilateral matrix equations of arbitrary order. For solutions which have perturbative expansions in the matrix coefficients, the solution and all its positive powers are sums of terms which are symmetrized in all the matrix coefficients and of terms which are commutators.

9 pages, LaTeX, no figures, theorem generalized and a new method of proof included

References in corpus (4)

• Nonlinear Self-Duality in Even Dimensions
• Duality Invariant Born-Infeld Theory
• Proof of a Symmetrized Trace Conjecture for the Abelian Born-Infeld Lagrangian
• Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem

Cited by in corpus (13)

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• N=2 Born-Infeld Attractors
• Nonlinear Self-Duality and Supergravity
• Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited
• On the dualization of Born-Infeld theories
• Generalized Born--Infeld Actions and Projective Cubic Curves
• Auxiliary superfields in N=1 supersymmetric self-dual electrodynamics
• A superfield constraint for N=2 --> N=0 breaking
• Proof of a Symmetrized Trace Conjecture for the Abelian Born-Infeld Lagrangian
• Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited: The U(N) Case
• Two-Field Born-Infeld with Diverse Dualities
• Properties of perturbative solutions of unilateral matrix equations
• Some remarks on unilateral matrix equations