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

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 pro...

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Bibliographic Details
Published in:arXiv.org 2000-04
Main Authors: Aschieri, Paolo, Brace, Daniel, Morariu, Bogdan, Zumino, Bruno
Format: Article
Language:English
Subjects:
Commutators
Field strength
Mathematical analysis
Matrix methods
Thermal expansion
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0003228