MASSLESS SCALAR FIELD PROPAGATOR IN A QUANTIZED SPACETIME

Abstract

We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H. S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex p2 plane and goes like 1/p2 as p2→0 from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as p2 increases to the discretization scale 1/a2and remains zero for p2>1/a2. This behaviour is consistent with the termination of single-particle propagation on the ultraviolet side of the discretization scale. The imaginary part of the propagator, consistent with a multiparticle-state spectral function branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when 1/a2<p2<∞. The multi-particle aspect of this spectral function within the Källen-Lehmann representation of the propagator leads to the interpretation that the propagation of free-fields in a quantized spacetime is analogous to propagation of interacting fields in a continuous spacetime.