Causality criteria

By causality of matter one means its property not to admitsuperluminal excitations, i.e. excitations that propagate faster than the vacuum speed of lightc. In discussing the propagation of small excitations, one has to distinguish betweenphase velocities _j /k, (1jg=number of dispersion branches),group velocities d _j /dk, a front velocityv _f : = and the propagation speedv _q :=(dp/d)^1/2 of isotropic quasistatic (small) perturbations. We discuss some of their properties. In particular, the (maximal) speedv _s of small signals is not smaller thanv _f , and equalsv _f whenever the dispersion branches _j (k) behave reasonably at infinity of the complexk-plane. In essence stronger conditions guaranteev _q <v _f (in which casev _q c would imply superluminal behaviour).