Abstract
The role of τγ5-gauge invariance in the theory of elementary particles proposed byNambu andJona-Lasinio (1) has been examined in the framework of the lowest ladder approximation followed by them. It has been shown that the above invariance property is not necessary for proving the vanishing of the pion mass in this approximation. Their integral equation for the axial vector vertex part needs some modification if the solution is to represent the vertex part of a conserved axial vector current.
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