Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem

Details Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem

2000-04-12

arxiv.org/abs/hep-th/0004088v2

Lett.Math.Phys. 52 (2000) 177-184

Physics

High Energy Physics

High Energy Physics - Theory

8 pages. Misprints corrected, references added

Scientific paper

We analyze the perturbation series for noncommutative eigenvalue problem $AX=X\lambda$ where $\lambda$ is an element of a noncommutative ring, $ A$ is a matrix and $X$ is a column vector with entries from this ring. As a corollary we obtain a theorem about the structure of perturbation series for Tr $x^r$ where $x$ is a solution of noncommutative algebraic equation (for $r=1$ this theorem was proved by Aschieri, Brace, Morariu, and Zumino, hep-th/0003228, and used to study Born-Infeld lagrangian for the gauge group $U(1)^k$).

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