Wave structure of Yang-Mills magnetohydrodynamics.

Abstract

The theory of chromohydrodynamics is considered in the limit of ideal magnetohydrodynamics. The question of causalty (all wave velocities less than the velocity of light) and well posedness (continuous dependence on initial data) are addressed. The analysis is based on a covariant and constraint-free divergence formulation of ideal Yang-Mills magnetohydrodynamics, following the author's earlier work (on Maxwell's equations). The characteristic equation which describes the velocities of the small amplitude waves is derived in terms of a sixth-order polynomial equation Y(U,${\ensuremath{\nu}}_{\mathit{a}}$)=0. The result shows that Alfv\`en waves (\ensuremath{\delta}P=\ensuremath{\delta}r=0) do not in general exist. We proceed by proving the well posedness of the initial value problems in ideal Yang-Mills magnetohydrodynamics, using a generalized Friedrichs-Lax symmetrization procedure. This establishes that the theory is causal and contains well-posed initial value problems. Our formal arguments show that large color conductivity in collective wave motion between the field and quarks in the presence of finite macroscopic background fields is permissible.