Embedded Space-Time and Particle Symmetries

Abstract

The bootstrap yields the strong-interactions symmetry provided the hadron currents participating in nonstrong interactions are first fed into it; the alternative course, in which the bootstrap is required to generate the entire symmetry uniquely, with no a priori information from the nonstrong interactions, seems to lie beyond the present techniques and would also leave unexplained the subsequent emergence of the weaker couplings. We suggest that "internal" symmetries may have a geometrical origin, corresponding to transformations in the global embedding space of the four-dimensional physical Riemann universe. These would be the unitary or orthogonal transformations of the normal subspace, since the latter do transform a small region of curved space-time into itself. This picture fits in with the short ranges of the strong interactions. Cosmological and astrophysical implications are noted.