Mass Inequalities in Vectorial Gauge.Theory Based on Compact Semi-simple Lie Group

The mass inequalities valid in the vectorial gauge theory based on a simple group can be generalized to the case with a compact semi-simple Lie group if the vacuum angle is assumed to be zero. A new meaning of these inequalities lies in that a vectorial Aavor gauge symmetry can not be spontaneously broken by the color condensates among the fermions with nonzero bare masses. In the semi-simple group case the vacuum angle could be naturally set to be zero only if there are massless fermions assigned in special representations of the group. This provides the possibility to break down the mass inequalities and could find some physical applications.