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Item Initial state of matter fields and trans-Planckian physics: Can CMB observations disentangle the two?(American Physical Society, 2005-05-17) Sriramkumar, L.; Padmanabhan, T.The standard, scale-invariant, inflationary perturbation spectrum will be modified if the effects of trans- Planckian physics are incorporated into the dynamics of the matter field in a phenomenological manner, say, by the modification of the dispersion relation. The spectrum also changes if we retain the standard dynamics but modify the initial quantum state of the matter field. We show that, given any spectrum of perturbations, it is possible to choose a class of initial quantum states which can exactly reproduce this spectrum with the standard dynamics.We provide an explicit construction of the quantum state which will produce the given spectrum. We find that the various modified spectra that have been recently obtained from ‘‘trans-Planckian considerations’’ can be constructed from suitable squeezed states above the Bunch- Davies vacuum in the standard theory. Hence, the CMB observations can, at most, be useful in determining the initial state of the matter field in the standard theory, but it can not help us to discriminate between the various Planck scale models of matter fields.We study the problem in the Schrodinger picture and determine the criterion for negligible back reaction due to modified initial conditions.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 Does a nonzero tunneling probability imply particle production in time-independent classical electromagnetic backgrounds?(American Physical Society, 1996-12-15) Sriramkumar, L.; Padmanabhan, T.In this paper, we probe the validity of the tunneling interpretation that is usually called forth in the literature to explain the phenomenon of particle production by time-independent classical electromagnetic backgrounds. We show that the imaginary part of the effective Lagrangian is zero for a complex scalar field quantized in a time-independent, but otherwise arbitrary, magnetic field. This result implies that no pair creation takes place in such a background. But we find that when the quantum field is decomposed into its normal modes in the presence of a spatially confined and time-independent magnetic field, there exists a nonzero tunneling prob-ability for the effective Schro¨dinger equation. According to the tunneling interpretation, this result would imply that spatially confined magnetic fields can produce particles, thereby contradicting the result obtained from the effective Lagrangian. This lack of consistency between these two approaches calls into question the validity of attributing a nonzero tunneling probability for the effective Schro¨dinger equation to the production of particles by the time-independent electromagnetic backgrounds. The implications of our analysis are discussed.Item Probes of vacuum structure of quantum fields in classical backgrounds(World Scientific Publishing Company, 2000-10-04) Sriramkumar, L.; Padmanabhan, T.We compare the different approaches presently available in literature to probe the vacuum structure of quantum fields in classical electromagnetic and gravitational back- grounds. We compare the results from the Bogolubov transformations and the effective Lagrangian approach with the response of monopole detectors (of the Unruh - DeWitt type) in noninertial frames in flat spacetime and in inertial frames in different types of classical electromagnetic backgrounds. We also carry out such a comparison in inertial and rotating frames when boundaries are present in flat spacetime. We find that the results from these different approaches do not, in general, agree with each other. We attempt to identify the origin of these differences and then go on to discuss its implications for classical gravitational backgrounds.Item Finite-time response of inertial and uniformly accelerated Unruh–DeWitt detectors(IOP Publishing, 1996-05-15) Sriramkumar, L.; Padmanabhan, T.We study the response of inertial and uniformly accelerated Unruh–DeWitt detectors in the Minkowski vacuum when they are coupled to the quantum field for a finite time interval. A finite-time detector will respond even on an inertial trajectory due to transient effects. Also, the response will depend on the manner in which the detector is switched on and off. We study the response for smooth as well as abrupt switching of the detector. The detectors are switched on and off with window functions whose width, T , determines the effective timescale for which the detector is coupled to the field. We work out in detail the response of inertial and uniformly accelerated detectors for Gaussian, exponential and rectangular window functions and also obtain a general formula for the response of these detectors when a window function is specified. The T ! 0 and T !1 limits are discussed in detail and several subtleties in the limiting procedure are clarifiedItem Possible quantum interpretation of certain power spectra in classical field theory(World Scientific Publication Company, 1997-03-13) Srinivasan, K.; Sriramkumar, L.; Padmanabhan, T.In this paper we report an analogue for the vacuum state in classical field theory and its Planckian nature with respect to uniformly accelerated observers. When a real, monochromatic, mode of a scalar field is Fourier analyzed with respect to the proper time of a uniformly accelerating observer, the resulting power spectrum consists of three terms none of which have a simple classical meaning. Specifically, the three terms are (i) a factor (1/2) that is typical of the ground state energy of a quantum ascillator, (ii) a Planckian distribution N(Ω) and — most importantly — (iii) a term , which is the root mean aquare fluctuations about the Planckian distribution. It is the appearance of the root mean square fluctuations that motivates us to attribute a "thermal" nature to the power spectrum. Such a power spectrum also arises when we Fourier analyze a real, monochromatic, plane electromagnetic wave in the frame of a uniformly accelerating observer. We also present a model of a detector whose response is the Fourier spectrum of the field with respect to its proper time, which illustrates that it should, in principle, be possible to physically measure the power spectrum we have obtained. These results show that some of the "purely" quantum mechanical results might have a classical analogue.Item Plane waves viewed from an accelerated frame: Quantum physics in a classical setting(American Physical Society, 1997-04-14) Srinivasan, K.; Sriramkumar, L.; Padmanabhan, T.We report here an analogue for the vacuum state in classical field theory and its Planckian nature with respect to uniformly accelerated observers. We find that when a real, monochromatic mode of a classical field is Fourier transformed with respect to the proper time of a uniformly accelerating observer, the resulting power spectrum has three separate terms none of which have a simple classical meaning. But they bear a striking resemblance to the quantum mechanical description. Specifically, the three terms are (i) a factor (1/2) that is typical of the ground state energy of a quantum oscillator, (ii) a Planckian distribution N(Ω) and, most importantly, (iii) a term proportional to √N(N+1), which is the root mean square fluctuations about the Planckian distribution. The implications of this result are discussed.Item 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.Item Nontrivial classical backgrounds with vanishing quantum corrections(American Physical Society, 1996-11-15) Sriramkumar, L.; Mukund, R.; Padmanabhan, T.Vacuum polarization and particle production effects in classical electromagnetic and gravitational back-grounds can be studied by the effective Lagrangian method. Background field configurations for which the effective Lagrangian is zero are special in the sense that the lowest order quantum corrections vanish for such configurations. We propose here the conjecture that there will be neither particle production nor vacuum polarization in classical field configurations for which all the scalar invariants are zero. We verify this conjec-ture, by explicitly evaluating the effective Lagrangian, for nontrivial electromagnetic and gravitational back-grounds with vanishing scalar invariants. The implications of this result are discussed.