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Dewitt, Charles W.; McCullough, M.

doi:10.1097/00007890-197504000-00006

Cited by 39 publications

(34 citation statements)

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“…In Schwinger's proper time formalism, the Feynman Green's function corresponding to such a scalar field can be expressed as [26,27] …”

Section: Path Integral Duality Modified Two-point Functionsmentioning

confidence: 99%

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Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation

Sriramkumar¹,

Shankaranarayanan²

2006

J. High Energy Phys.

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The enormous red-shifting of the modes during the inflationary epoch suggests that physics at the Planck scale may modify the standard, nearly, scale-invariant, primordial, density perturbation spectrum. Under the principle of path-integral duality, the space-time behaves as though it has a minimal length L P (which we shall assume to be of the order of the Planck length), a feature that is expected to arise when the quantum gravitational effects on the matter fields have been taken into account. Using the method of path integral duality, in this work, we evaluate the Planck scale corrections to the spectrum of density perturbations in the case of exponential inflation. We find that the amplitude of the corrections is of the order of (H/M P ), where H and M P denote the inflationary and the Planck energy scales, respectively. We also find that the corrections turn out to be completely independent of scale. We briefly discuss the implications of our result, and also comment on how it compares with an earlier result.

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“…In Schwinger's proper time formalism, the Feynman Green's function corresponding to such a scalar field can be expressed as [26,27] …”

Section: Path Integral Duality Modified Two-point Functionsmentioning

confidence: 99%

“…On substituting the wave function (27) in the expression (33) for the modified power spectrum and imposing the condition of Hubble exit, we obtain that…”

Section: Planck Scale Corrections Due To Path Integral Dualitymentioning

confidence: 99%

Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation

Sriramkumar¹,

Shankaranarayanan²

2006

J. High Energy Phys.

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“…As the black hole settles down to a stationary state on the time slice Σ, the mixed state ρ ext can be shown (via non-trivial calculation [8]) to approach precisely a thermal state ρ H at the Hawking temperature T H = c 3 /(8πk B GM ), where M is the hole's mass. As long as the back action of the Hawking radiation on spacetime is negligible (an eternal black hole), matter remains in the pure state |Ψ Σ , which unitarily evolves to become entangled with its collapsed half inside the emerging event horizon.…”

Section: Black-hole Evaporation and Non-standard Quantum Mechanicsmentioning

confidence: 99%

Signalling, entanglement and quantum evolution beyond Cauchy horizons

Yurtsever¹,

Hockney²

2004

Class. Quantum Grav.

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Consider a bipartite entangled system half of which falls through the event horizon of an evaporating black hole, while the other half remains coherently accessible to experiments in the exterior region. Beyond complete evaporation, the evolution of the quantum state past the Cauchy horizon cannot remain unitary, raising the questions: How can this evolution be described as a quantum map, and how is causality preserved? What are the possible effects of such nonstandard quantum evolution maps on the behavior of the entangled laboratory partner? More generally, the laws of quantum evolution under extreme conditions in remote regions (not just in evaporating black-hole interiors, but possibly near other naked singularities and regions of extreme spacetime structure) remain untested by observation, and might conceivably be non-unitary or even nonlinear, raising the same questions about the evolution of entangled states. The answers to these questions are subtle, and are linked in unexpected ways to the fundamental laws of quantum mechanics. We show that terrestrial experiments can be designed to probe and constrain exactly how the laws of quantum evolution might be altered, either by black-hole evaporation, or by other extreme processes in remote regions possibly governed by unknown physics. OverviewStandard proofs that non-local Bell correlations [1] between parts of an entangled system cannot be used to acausally signal (transfer information) rely on quantum evolution being everywhere unitary. However, as Hawking [2] first pointed out when he gave examples of non-unitary but causal maps for evaporating black holes, unitarity, a sufficient but not a necessary condition for causality, may break down in the late stages of black-hole evaporation. In this paper we ask: When entangled systems partly cross the event horizons of evaporating black holes (or Cauchy horizons of other, more general naked singularities) and partly remain coherently accessible to experiments outside, what constraints on their non-unitary, and possibly nonlinear quantum evolution would ensure causality? and: Can signaling (acausal) evolution be detected at large distances if it indeed does take place under the extreme conditions near naked singularities and evaporating black-hole interiors?It turns out, as we will show below, that linearity (along with probability conservation and locality) is sufficient to preserve causality; acausal signaling is possible only with nonlinear maps. Nonlinear generalizations of quantum mechanics and their implications for measurement theory and causality have been discussed by many authors [3]; it is not our goal in this paper to contribute to these formal developments. We adopt the conservative position that at most a minimal generalization of quantum theory-namely one that allows for the possibility of nonlinear quantum maps while keeping the rest of the formalism intact-is necessary to understand the implications of non-standard quantum dynamics for entangled states. There is, of course, no experimental evide...

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“…This is not in fact a new problem. DeWitt (1975) has pointed out that in any nonstationary spacetime it is impossible to define a T  that is simultaneously normal ordered in both the "in" and "out" regions, has matrix elements which are smooth functions, and has a divergence which vanishes everywhere. According to DeWitt, the correct procedure is to give up the normal ordering and use a subtraction procedure that respects the conservation equation…”

Section: Regularization and Renormalization In The Effective Actionmentioning

confidence: 99%

Untitled

Camp

Safko

2000

International Journal of Theoretical Physics

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An alternative inflationary model is proposed predicated upon a consideration of the form of the uncertainty principle in a curved background spacetime. An argument is presented suggesting a possible curvature dependence in the correct commutator relations for a quantum field in a classical background which cannot be deduced by simply extrapolation from the flat spacetime theory. To assess the possible consequences of this dependence, we apply the idea to a scalar field in a closed FriedmannRobertsonWalker background, using a simple model for the curvature dependence (along the way, a previous result obtained by Bunch (1980) for the adiabatically expanded wave function is corrected). The result is a timedependent cosmological constant, producing a vast amount of inflation that is independent of the mass of the matter field or its effective potential. Furthermore, it is seen that the field modes are initially zero for all wavelengths and come into being as the universe evolves. In this sense, the universe creates its contents out of its own expansion. At the end of the process, the matter field is far from equilibrium and essentially reproduces the initial conditions for the New Inflationary Model.

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Cited by 39 publications

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Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation

Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation

Signalling, entanglement and quantum evolution beyond Cauchy horizons

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