Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-04-21
Phys.Rev.D80:044005,2009
Physics
High Energy Physics
High Energy Physics - Theory
v1. 10 pages, no figures; v2. 11 pages, acknowledgments added
Scientific paper
10.1103/PhysRevD.80.044005
The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length, $\lp$, in a {\it locally Lorentz invariant manner}. We use this prescription to evaluate the duality modified propagators in spacetimes with {\it constant curvature} (exactly in the case of one spacetime, and in the Gaussian approximation for another two), and show that: (i) the modified propagators are ultra violet finite, (ii) the modifications are {\it non-perturbative} in $\lp$, and (iii) $\lp$ seems to behave like a `zero point length' of spacetime intervals such that $\l< \sigma^2(x,x')\r> = \l[\sigma^{2}(x,x')+ {\cal O}(1) \lp^2 \r]$, where $\sigma(x,x')$ is the geodesic distance between the two spacetime points $x$ and $x'$, and the angular brackets denote (a suitable) average over the quantum gravitational fluctuations. We briefly discuss the implications of our results.
Kothawala Dawood
Padmanabhan Thanu
Shankaranarayanan S.
Sriramkumar L.
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