Unique effective action in two dimensional induced quantum gravity

Odintsov, Sergei D.; Шевченко, И. Н.

doi:10.1007/bf01555530

Cited by 4 publications

(6 citation statements)

References 10 publications

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“…This technique applies only to some restricted class of operators called minimal operators. Although the technique can be extended to non-minimal operators as well following the work of Barvinsky and Vilkovisky [29] (see [11,[30][31][32][33][34][35] for its applications), it is still very difficult to implement it in practice. As such we resort to the perturbative expansion technique as follows (for application of this technique see [12,25,36,37]).…”

Section: Some Essential Preliminaries For the Computation Of Divergen...mentioning

confidence: 99%

Local momentum space: scalar field and gravity

Panda,

Tinwala,

Vidyarthi

2023

Class. Quantum Grav.

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We use the local momentum space technique to obtain an expansion of the Feynman propagatorsfor scalar field and graviton up to first order in the background curvature. The expressions for thepropagators are cross-checked with the past literature as well as with the expressions for the tracedheat kernel coefficients. The propagators so obtained are used to compute one-loop divergences inthe Vilkovisky-Dewitt’s effective action for a scalar field non-minimally coupled with gravity for anarbitrary spacetime metric background. The Vilkovisky-DeWitt effective action is then comparedwith the standard effective action in the limit κ = 0, where κ = 2/MP in terms of the Planck mass. An important inference is drawn following the comparison. The comparison yields the important result that taking the limit κ = 0 after computing the Vikovisky-DeWitt effective action is not equivalent to computing the Vikovisky-DeWitt effective action for the same theory in the absence of gravity.

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Section: Some Essential Preliminaries For the Computation Of Divergen...mentioning

confidence: 99%

Local momentum space: scalar field and gravity

Panda,

Tinwala,

Vidyarthi

2023

Class. Quantum Grav.

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“…and then employ heat kernel technique [17,19] to compute the divergences in effective action. However, this technique is applicable to some restricted class of operators called minimal operators and can, in certain cases, be extended to non-minimal ones following the work of Barvinsky & Vilkovisky [20] (see [21][22][23][24][25][26][27] for its applications). Owing to a highly non-trivial form of the operator, we instead resort to the perturbative expansion technique.…”

Section: Some Essential Preliminaries For Computation Of Divergences ...mentioning

confidence: 99%

Local momentum space: Scalar field and gravity

Panda¹,

Altafhussain²,

Vidyarthi³

2022

Preprint

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We use the local momentum space technique to obtain an expansion of the Feynman propagators for scalar field and graviton up to first order in curvature. The expressions for propagators are cross-checked with the past literature as well as with the expressions for the traced heat kernel coefficients. The propagators so obtained are used to compute one loop divergences in Vilkovisky-Dewitt's effective action for a scalar field minimally coupled with gravity for arbitrary space-time background.

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“…[8], where the path integral (2) without torsion and in the self-dual limit ρ 0 → ∞ has been studied. Presumably, such limit describes the infrared dynamics of four-dimensional quantum gravity [9] (see also [10]). When ρ 0 → ∞, the path integral over g µν becomes the integral over conformally self-dual metrics.…”

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confidence: 99%

“…where the last term in both brackets is the contribution of ∆ to the conformal anomaly [10,12], and the last terms in (14) and (15) are the a 0 + a L and b 0 + b L found in [12], respectively. These contributions are equal to the trace anomaly coefficients of conformal quantum gravity 3 (see ref.…”

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confidence: 99%