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The particles interaction in the 2 + 1 topologically massive gauge theories is given. It turns out, that contrary to the usual case, two equally charged particles (fermions or the non-Abelian topologically massive vector bosons) attract each other, not repulse. This attraction can lead in principle to vacuum instability, in which we will use some trial wave function techniques. Possible applications are briefly discussed. 12 refs., 9 figs.

The equal charges attraction in the 2 + 1 topologically massive gauge theories and possible vacuum instability