Abstract
In a previous paper a scalar-conformal derivative (SCD) was derived. In this paper we investigate the properties of SCD, showing that when the kinetic energy is expressed in terms of SCD, the trace of the canonical energy-momentum tensor is soft (zero for conformal Lagrangians). For Lagrangians which are both chirally and conformally invariant, the SCD can be reduced to a simple derivative by using the relation ${\ensuremath{\chi}}^{2}={\ensuremath{\pi}}^{2}+{\ensuremath{\sigma}}^{2}$ when the chiral symmetry is realized linearly. In the nonlinear realization of chiral symmetry, for chirally and conformally invariant Lagrangians, the SCD is in agreement with Isham et al. Also, the breaking of a nonlinearly realized chiral symmetry is discussed. When chiral symmetry is broken, one finds that the mass of the $\ensuremath{\pi}$ field is proportional to the mass of the $\ensuremath{\chi}$ field. The proportionality constant is shown to be related to the normalization one chooses for the chiral covariant derivative.
Published Version
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