Compositeness condition at the next-to-leading order in the Nambu-Jona-Lasinio model

Exact scale invariance of composite-field coupling constants

We show that the coupling-constant of a quantum-induced composite field is scale invariant due to its compositeness condition. It is first demonstrated in next-to-leading order in 1/N in typical models, and then we argue that it holds exactly.

Lorentz invariance and origin of symmetries

We reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can be imposed only in the sense that all Lorentz noninvariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. The application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symmetry in both Abelian and non-Abelian cases. In contrast, purely global symmetries are generated only as accidental consequences of the gauge symmetry.