Feynman propagator in curved spacetime: A momentum-space representation

Bunch, T S; Parker, Leonard

doi:10.1103/physrevd.20.2499

Cited by 296 publications

(325 citation statements)

References 7 publications

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“…We note that a term of the form ξ 2 Rϕ 2 is required by renormalization for a purely quantized scalar field ϕ if a self-interaction term of the form λ 4! ϕ 4 appears in the bare Lagrangian density [34,35]. Here we have found that the Yukawa interaction demands the presence of the renormalized terms ξ 1 Rϕ and ξ 2 Rϕ 2 (as well as the terms λ i ϕ i ), even if they are not present in the bare Lagrangian density.…”

Section: Ultraviolet Divergences and Renormalization Countertermsmentioning

confidence: 79%

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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Section: Ultraviolet Divergences and Renormalization Countertermsmentioning

confidence: 79%

Adiabatic regularization with a Yukawa interaction

et al. 2017

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“…Note that we have chosen the notation to emphasize the fact that the effective action depends on the background field in two ways: explicitly through φ b , and implicitly through g(φ b ). The key point (more or less equivalent to Sakharov's "induced gravity" proposal) is that defining the determinant requires both regularization and renormalization, and that doing so introduces counterterms proportional to the first d/2 Seeley-DeWitt coefficients [49,50,51,52]. The form of these counterterms is well-known, and in fact for the second-order differential operator…”

Section: Induced Gravitymentioning

confidence: 99%

Analogue gravity from field theory normal modes?

Barceló¹,

Liberati²,

Visser³

2001

Class. Quantum Grav.

109

194

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We demonstrate that the emergence of a curved spacetime "effective Lorentzian geometry" is a common and generic result of linearizing a classical scalar field theory around some non-trivial background configuration. This investigation is motivated by considering the large number of "analog models" of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (that is, a field theoretic "normal mode analysis") results in fluctuations whose propagation is governed by a Lorentzian-signature curved spacetime "effective metric". In the simple situation considered in this paper, (a single classical scalar field), this procedure results in a unique effective metric, which is quite sufficient for simulating kinematic aspects of general relativity (up to and including Hawking radiation). Upon quantizing the linearized fluctuations around this background geometry, the one-loop effective action is guaranteed to contain a term proportional to the Einstein-Hilbert action of general relativity, suggesting that while classical physics is responsible for generating an "effective geometry", quantum physics can be argued to induce an "effective dynamics". The situation is strongly reminiscent of, though not identical to, Sakharov's "induced gravity" scenario, and suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics. (We mean this in the same sense that hydrodynamics is a long-distance emergent phenomenon, many of whose predictions are insensitive to the short-distance cutoff implicit in molecular dynamics.)

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“…If the spacetime is topologically trivial and consists of one patch covered by conformally flat coordinates, then the minimally coupled massless Green function equals the flat spacetime Green function (10).…”

Section: =mentioning

confidence: 99%

Scalar field Green functions on causal sets

Nomaan

Dowker

Surya

2017

Class. Quantum Grav.

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We examine the validity and scope of Johnston's models for scalar field retarded Green functions on causal sets in 2 and 4 dimensions. As in the continuum, the massive Green function can be obtained from the massless one, and hence the key task in causal set theory is to first identify the massless Green function. We propose that the 2-d model provides a Green function for the massive scalar field on causal sets approximated by any topologically trivial 2 dimensional spacetime. We explicitly demonstrate that this is indeed the case in a Riemann normal neighbourhood. In 4-d the model can again be used to provide a Green function for the massive scalar field in a Riemann normal neighbourhood which we compare to Bunch and Parker's continuum Green function. We find that the same prescription can also be used for deSitter spacetime and the conformally flat patch of anti deSitter spacetime. Our analysis then allows us to suggest a generalisation of Johnston's model for the Green function for a causal set approximated by 3 dimensional flat spacetime.

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Feynman propagator in curved spacetime: A momentum-space representation

Cited by 296 publications

References 7 publications

Adiabatic regularization with a Yukawa interaction

Adiabatic regularization with a Yukawa interaction

Analogue gravity from field theory normal modes?

Scalar field Green functions on causal sets

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