Renormalization of a Classical Gravitational Field Interacting with Quantized Matter Fields

Utiyama, Ryôyû; DeWitt, Bryce S.

doi:10.1063/1.1724264

Cited by 477 publications

(517 citation statements)

References 1 publication

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“…These divergences are similar to those described in [32]. To characterize them, one plugs in (41)-(42) the adiabatic expansion of h I k and h II k , given in Eq.…”

Section: Renormalization Of the Stress-energy Tensor T µν And Thementioning

confidence: 94%

Adiabatic regularization with a Yukawa interaction

et al. 2017

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We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between quantized Dirac fermions and a homogeneous background scalar field. We give explicit expressions for the renormalized expectation values of the stressenergy tensor T µν and the bilinear ψ ψ in a spatially flat Friedmann-Lemaitre-RobertsonWalker (FLRW) spacetime. These are basic ingredients in the semiclassical field equations of fermionic matter in curved spacetime interacting with a background scalar field. The ultraviolet subtracting terms of the adiabatic regularization can be naturally interpreted as coming from appropriate counterterms of the background fields. We fix the required covariant counterterms. To test our approach we determine the contribution of the Yukawa interaction to the conformal anomaly in the massless limit and show its consistency with the heat-kernel method using the effective action.

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“…These divergences are similar to those described in [32]. To characterize them, one plugs in (41)-(42) the adiabatic expansion of h I k and h II k , given in Eq.…”

Section: Renormalization Of the Stress-energy Tensor T µν And Thementioning

confidence: 94%

Adiabatic regularization with a Yukawa interaction

et al. 2017

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“…The predicted magnitudes of these effects are obtained through renormalization of fields and coupling constants, which absorb the infinities in a covariant manner. Renormalization methods have long been extended to quantized fields propagating in the curved spacetime of general relativity [6] (see also [7] and references therein), but predicted quantum vacuum effects of curved spacetime have been too small to be directly observed. Quantum vacuum effects in curved spacetimes have also been explored in connection with particle creation by the expansion of the universe and by black holes [8,9].…”

Section: Introductionmentioning

confidence: 99%

Erratum: New quantum aspects of a vacuum-dominated universe [Phys. Rev. D62, 083503 (2000)]

Parker¹,

Raval²

2003

Phys. Rev. D

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In a new model that we proposed, nonperturbative vacuum contributions to the effective action of a free quantized massive scalar field lead to a cosmological solution in which the scalar curvature becomes constant after a time tj (when the redshift z ∼ 1) that depends on the mass of the scalar field and its curvature coupling. This spatially-flat solution implies an accelerating universe at the present time and gives a good one-parameter fit to high-redshift Type Ia supernovae (SNe-Ia) data, and the present age and energy density of the universe. Here we show that the imaginary part of the nonperturbative curvature term that causes the cosmological acceleration, implies a particle production rate that agrees with predictions of other methods and extends them to non-zero mass fields. The particle production rate is very small after the transition and is not expected to alter the nature of the cosmological solution. We also show that the equation of state of our model undergoes a transition at tj from an equation of state dominated by non-relativistic pressureless matter (without a cosmological constant) to an effective equation of state of mixed radiation and cosmological constant, and we derive the equation of state of the vacuum. Finally, we explain why nonperturbative vacuum effects of this ultralow-mass particle do not significantly change standard early universe cosmology.

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“…The first two terms have been calculated explicitly as χ 1 = 1/2 and χ 2 = 3/4 [37,12]. 2 We have then shown that these are universal values independent of the gauge group and the contents of matter fields as far as they are conformally coupled. 3 The bare quantity t 0 is a single dimensionless gravitational coupling constant, while b 0 is not an independent coupling as mentioned below.…”

Section: Quantum Gravity Actionmentioning

confidence: 99%

“…The quantization of gravity based on the Einstein action [2,3,4] has a lot of difficulties. First of all, the theory is not renormalizable.…”

Section: Introductionmentioning

confidence: 99%

Physical cosmological constant in asymptotically background-free quantum gravity

Hamada

Matsuda

2017

Phys. Rev. D

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We study the effective potential in renormalizable quantum gravity with a single dimensionless conformal coupling without a Landau pole. In order to describe a background-free dynamics at the Planck scale and beyond, the conformal-factor field is quantized exactly in a nonperturbative manner. Since this field does not receive renormalization, the field-independent constant in the effective potential becomes itself invariant under the renormalization group flow. That is to say, it gives the physical cosmological constant. We explicitly calculate the physical cosmological constant at the one-loop level in the Landau gauge. We find that it is given by a function of renormalized quantities of the cosmological constant, the Planck mass and the coupling constant, and it should be the observed value. It will give a new perspective on the cosmological constant problem free from an ultraviolet cutoff.

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Renormalization of a Classical Gravitational Field Interacting with Quantized Matter Fields

Cited by 477 publications

References 1 publication

Adiabatic regularization with a Yukawa interaction

Adiabatic regularization with a Yukawa interaction

Erratum: New quantum aspects of a vacuum-dominated universe [Phys. Rev. D62, 083503 (2000)]

Physical cosmological constant in asymptotically background-free quantum gravity

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