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Author: search.filters.author.Shankaranarayanan, S.

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    Hypothesis of path integral duality: Applications to QED
    (World Scientific Publishing Company, 2000-06-16) Shankaranarayanan, S.; Padmanabhan, T.
    We use the modi ed propagator for quantum eld based on a \principle of path integral duality" proposed earlier in a paper by Padmanabhan to investigate several results in QED. This procedure modi es the Feynman propagator by the introduction of a fundamental length scale. We use this modi ed propagator for the Dirac particles to evaluate the rst order radiative corrections in QED. We nd that the extra factor of the modi ed propagator acts like a regulator at the Planck scales thereby removing the divergences that otherwise appear in the conventional radiative correction calculations of QED. We nd that: (i) all the three renormalization factors Z1, Z2, and Z3 pick up nite corrections and (ii) the modi ed propagator breaks the gauge invariance at a very small level of O(10−45). The implications of this result to generation of the primordial seed magnetic elds are discussed.
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    Hawking radiation in different coordinate settings: complex paths approach
    (IOP Publishing, 2002-04-30) Shankaranarayanan, S.; Padmanabhan, T.; Srinivasan, K.
    We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild spacetime. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semiclassical action. This singularity is regularized by using the method of complex paths and we find that Hawking radiation is recovered in these coordinates indicating the covariance of Hawking radiation as far as these coordinates are concerned.
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    Method of complex paths and general covariance of Hawking radiation
    (World Scientific Publishing Company, 2001-02-05) Shankaranarayanan, S.; Srinivasan, K.; Padmanabhan, T.
    We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space{time. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semiclassical action. This singularity is regularized by using the method of complex paths and we find that Hawking radiation is recovered in these coordinates indicating the covariance of Hawking radiation. This also shows that there is no correspondence between the particles detected by the model detector and the particle spectrum obtained by the quantum field theoretic analysis | a result known in other contexts as well.
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    Vanishing of the cosmological constant in nonfactorizable geometry
    (American Physical Society, 2001-04-26) Padmanabhan, T.; Shankaranarayanan, S.
    We generalize the results of Randall and Sundrum to a wider class of four-dimensional space-times includ-ing the four-dimensional Schwarzschild background and de Sitter universe. We solve the equation for graviton propagation in a general four dimensional background and find an explicit solution for a zero mass bound state of the graviton. We find that this zero mass bound state is normalizable only if the cosmological constant is strictly zero, thereby providing a dynamical reason for the vanishing of cosmological constant within the context of this model. We also show that the results of Randall and Sundrum can be generalized without any modification to the Schwarzschild background.
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    Path integral duality modified propagators in spacetimes with constant curvature
    (American Physical Society, 2009-08-10) Kothawala, Dawood; Sriramkumar, L.; Shankaranarayanan, S.; Padmanabhan, T.
    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 locally Lorentz invariant manner. We use this prescription to evaluate the duality modified propagators in spacetimes with 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 ultraviolet finite, (ii) the modifications are nonperturbative in LP, and (iii) LP seems to behave like a "zero point length" of spacetime intervals such that σ2(x,x') =[σ2(x,x')+O(1)LP2], where σ(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.