Does the axial vector current influence space-time?

In part icle physics the axial vector current, together with the vector current, has p layed an impor tant role in current algebras (1) and chiral dynamics (2). Does i t p lay any role in other branch of physics? In this let ter we argue tha t the axial vector current, along with the energy-momentum tensor, of the spin89 baryons and leptons may influence the space-time structure through the spin angular-momentum tensor contribut ing to gravi tat ional sources. In high-energy physics both the mass and spin of the hadrons are dynamical ly incorporated into the concept of Regge poles which has been successful in analysing the scattering data. On a macroscopic scale, however, the spin will p lay no significant role as well as the electric charges. Therefore i t appears quite reasonable tha t Einstein 's macroscopic theory of gravi ta t ion lets the mass, or the stress tensor, of macroscopic bodies alone be a unique source of gravi ta t ion and at the same t ime lets i t be a sole agency in generating a curved space-time. If we take such a microscopic viewpoint as that by which gravi tat ion arises through individual nucleons and electrons, or more generally spin89 baryons and leptons, s traightforward extrapolation of Einstein 's idea to the realm of part icle physics would not be justified. In this circumstance we would rather think that the mass and spin, or the energy-momentum tensor and spin angular-momentum tensor, are both contributing to gravi tat ional sources and hence have influence on the space-time structure. In order to avoid unnecessary confusion we emphasize the macroscopic nature of Einstein 's gravi ta t ional field equations. The stress tensor of macroscopic bodies appearing therein as a source tensor of gravi tat ion is represented by macroscopic observables, for example, the energy density, the fluid velocity and the pressure in the perfect-fluid model of a star. This stress tensor has nothing to do with the energy-momentum tensor of individual hadrons and leptons, except for tha t of the electromagnetic field which has a macroscopic and classical l imit . Hence it would be incorrect to judge our theory to be developed below as an alternative theory to Einstein's. I t must be remembered tha t two theories stand on a different scale, one microscopic and the other macroscopic, and tha t a relation between two could be established by taking the macroscopic limiting