Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-03-14
Int.J.Mod.Phys.E16:51-58,2007
Physics
High Energy Physics
High Energy Physics - Theory
6 pages, 1 eps figure embedded in manuscript
Scientific paper
10.1142/S0218301307004886
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 $p^2$ plane and goes like $1/p^2$ as $p^2\to 0$ from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as $p^2$ increases to the discretization scale $1/a^2$ and remains zero for $p^2>1/a^2$. 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-production branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when $1/a^2
Elias Victor
~Steele ~G. T.
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