On the effective character of a non-abelian DBI action

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 ν 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→+∞ limit. There are also some computations that could be of some interest in Relativistic Statistical Mechanics.