On the effective character of a non abelian DBI action

TL;DR

This paper explores how Lorentz covariance can emerge from Matrix Theory and non-abelian DBI actions, analyzing asymptotic expansions and their implications for M-theory and relativistic statistical mechanics.

Contribution

It provides insights into reconstructing Lorentz covariance from Matrix Theory through analysis of non-abelian DBI actions and asymptotic expansions of Bessel functions.

Findings

Analysis of asymptotic expansion of Bessel functions in amplitude computations.

Insights into Lorentz covariance emergence in the N→∞ limit.

Potential applications in relativistic statistical mechanics.

Abstract

We study the way Lorentz covariance can be reconstructed from Matrix Theory as a IMF description of M-theory. The problem is actually related to the interplay between a non abelian Dirac-Born-Infeld action and Super-Yang-Mills as its generalized non-relativistic approximation. All this physics shows up by means of an analysis of the asymptotic expansion of the Bessel functions $K_\nu$ that profusely appear in the computations of amplitudes at finite temperature and solitonic calculations. We hope this might help to better understand the issue of getting a Lorentz covariant formulation in relation with the $N\to +\infty$ limit. There are also some computations that could be of some interest in Relativistic Statistical Mechanics.