Research Publications
Permanent URI for this communityhttp://localhost:4000/handle/11007/1
Browse
2 results
Search Results
Item Hypothesis of path integral duality. II. Corrections to quantum field theoretic results(American Physical Society, 1998-07-13) Srinivasan, K.; Sriramkumar, L.; Padmanabhan, T.In the path integral expression for a Feynman propagator of a spinless particle of mass m, the path integral amplitude for a path of proper length R(x,x'\|gμν) connecting events x and x' in a spacetime described by the metric tensor gμν is exp \{-[m R(x,x'\|gμν)]\}. In a recent paper, assuming the path integral amplitude to be invariant under the duality transformation R-->(L2P/R), Padmanabhan has evaluated the modified Feynman propagator in an arbitrary curved spacetime. He finds that the essential feature of this ``principle of path integral duality'' is that the Euclidean proper distance (Δx)2 between two infinitesimally separated spacetime events is replaced by [(Δx)2+4L2P]. In other words, under the duality principle the spacetime behaves as though it has a ``zero-point length'' LP, a feature that is expected to arise in a quantum theory of gravity. In Schwinger's proper time description of the Feynman propagator, the weightage factor for a path with a proper time s is exp [-(m2s)]. Invoking Padmanabhan's ``principle of path integral duality'' corresponds to modifying the weightage factor exp [-(m2s)] to exp \{-[m2s+(L2P/s)]\}. In this paper, we use this modified weightage factor in Schwinger's proper time formalism to evaluate the quantum gravitational corrections to some of the standard quantum field theoretic results in flat and curved spacetimes. In flat spacetime, we evaluate the corrections to (1) the Casimir effect, (2) the effective potential for a self-interacting scalar field theory, (3) the effective Lagrangian for a constant electromagnetic background and (4) the thermal effects in Rindler coordinates. In arbitrary curved spacetime, we evaluate the corrections to (1) the effective Lagrangian for the gravitational field and (2) the trace anomaly. In all these cases, we first briefly present the conventional result and then go on to evaluate the corrections with the modified weightage factor. We find that the extra factor exp [-(L2P/s)] acts as a regulator at the Planck scale thereby ``removing'' the divergences that otherwise appear in the theory. Finally, we discuss the wider implications of our analysis.Item 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.