On the effective character of a non-abelian DBI action

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-InfeId 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 Ky 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 --> +infinity limit. There are also some computations that could be of some interest in Relativistic Statistical Mechanics. (C) 2001 Published by Elsevier Science B.V.