Lorentz-invariant membranes and finite matrix approximations

TL;DR

This paper investigates the preservation of Lorentz invariance in finite matrix models of relativistic membranes, revealing limitations at small N and exploring symmetry restoration as N increases.

Contribution

It demonstrates the impossibility of certain classical Lorentz invariance features at small N and studies how symmetry is recovered in the large N limit through numerical analysis.

Findings

Lorentz invariance cannot be fully realized for NxN matrices at N=2 or 3

Numerical evidence shows symmetry restoration as N approaches infinity

Finite N approximations have inherent limitations in capturing full Lorentz invariance

Abstract

The question of Lorentz invariance for finite N approximations of relativistic membranes is addressed. We find that one of the classical manifestations of Lorentz-invariance is not possible for NxN matrices (at least when N=2 or 3). How the symmetry is restored in the large N limit is studied numerically.