Thursday, July 25, 2013

1307.5618 (Dawood Kothawala)

Minimal Length and Small Scale Structure of Spacetime    [PDF]

Dawood Kothawala
Many generic arguments support the existence of a minimum spacetime interval L_0. Such a "zero-point" length can be naturally introduced in a locally Lorentz invariant manner via Synge's world function bi-scalar \Omega(p,P) which measures squared geodesic interval between spacetime events p and P. I show that there exists a \emph{non-local} deformation of spacetime geometry given by a \emph{disformal} coupling of metric to the bi-scalar \Omega(p,P), which yields a geodesic interval of L_0 in the limit p -> P. Locality is recovered when \Omega(p,P) >> L_0^2/2. I discuss several conceptual implications of the resultant small-scale structure of spacetime for QFT propagators as well as spacetime singularities.
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