Propagators for arbitrary spin in an einstein universe

Abstract

The evolution properties of arbitrary-spin classical fields in an Einstein Universe are determined, at least in principle. A second-order propagation equation is used for both massless and massive fields but is shown to be misleading for the former, essentially because it is not conformally invariant. The massive case presents the unexpected feature of a “tachyonic mass gap.” For example, for integral spin, j, if the mass lies between zero and a −1 j ( a is the radius of the spatial section of the universe) the propagator develops imaginary mass poles due to the coupling of the spin and the metric. This gives rise to exponentially diverging propagation functions in the classical case and, possibly, to causality violations in the quantized theory. The calculation involves a generalization of Schwinger's spherical harmonics with operator arguments and a continuation of Racah coefficients off the angular-momentum shell.