Group averaging for de Sitter free fields

Marolf, Donald; Morrison, Ian A.

doi:10.1088/0264-9381/26/23/235003

Cited by 34 publications

(48 citation statements)

References 52 publications

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“…We should also comment on the apparent conflict of our result with the pro-invariance argument given by Marolf and Morrison [63], based on work by Higuchi [64]. They dealt with free dynamical gravitons in a noncovariant gauge on the full de Sitter manifold and they were able to construct the complete panoply of mode solutions and inner products.…”

Section: Discussionmentioning

confidence: 58%

The graviton propagator in de Donder gauge on de Sitter background

Miao

Tsamis

Woodard

2011

Journal of Mathematical Physics

121

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We construct the graviton propagator on de Sitter background in exact de Donder gauge. We prove that it must break de Sitter invariance, just like the propagator of the massless, minimally coupled scalar. Our explicit solutions for its two scalar structure functions preserve spatial homogeneity and isotropy so that the propagator can be used within the larger context of inflationary cosmology, however, it is simple to alter the residual symmetry. Because our gauge condition is de Sitter invariant (although no solution for the propagator can be) renormalization should be simpler using this propagator than one based on a noncovariant gauge. It remains to be seen how other computational steps compare.

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Section: Discussionmentioning

confidence: 58%

The graviton propagator in de Donder gauge on de Sitter background

Miao

Tsamis

Woodard

2011

Journal of Mathematical Physics

121

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“…However, as already pointed out, thanks to the mathematical structure of the formulation we are using, inspired by the ambient space approach, it can be checked quite easily that the aforementioned break down in the normalization factor is because of a degeneracy for L = 0 mode reflecting the gauge-like symmetry (2). This point explicitly reveals that, quite contrary to the authors claim in [33][34][35][36][37][38][39][40][41][42][43][44][45][46], such a construction in the STT gauge conditions (L ≥ 2), by ignoring the L = 0 mode and consequently the gauge-like symmetry (2) reflected by it, does not transform correctly under the whole symmetries of the classical theory, and therefore, even obtaining an infrared free graviton twopoint function in this way is not physically significant since it is not covariant anyway. To see other criticism to this method, one can refer to [51][52][53][54][55].…”

Section: Graviton Two-point Functionmentioning

confidence: 80%

“…Take a closer look at the method which has been utilized in Refs. [33][34][35][36][37][38][39][40][41][42][43][44][45][46] shows that the authors have considered the synchronous-transversetraceless (STT) gauge to evaluate the graviton two-point function. The critical point associated with this method is that it is not possible to find a dS graviton field satisfying the STT gauge conditions if L = 0 or 1 [47].…”

Section: Graviton Two-point Functionmentioning

confidence: 99%

Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime

et al. 2019

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In a recent Letter, we have pointed out that the linearized Einstein gravity in de Sitter (dS) spacetime besides the spacetime symmetries generated by the Killing vectors and the evident gauge symmetry also possesses a hitherto 'hidden' local (gauge-like) symmetry which becomes anomalous on the quantum level. This gauge-like anomaly makes the theory inconsistent and must be canceled at all costs. In this companion paper, we first review our argument and discuss it in more detail. We argue that the cancelation of this anomaly makes it impossible to preserve dS symmetry in linearized quantum gravity through the usual canonical quantization in a consistent manner. Then, demanding that all the classical symmetries to survive in the quantized theory, we set up a coordinate-independent formalismà la Gupta-Bleuler which allows for preserving the (manifest) dS covariance in the presence of the gauge and the gauge-like invariance of the theory. On this basis, considering a new representation of the canonical commutation relations, we present a graviton quantum field on dS space, transforming correctly under isometries, gauge transformations, and gauge-like transformations, which acts on a state space containing a vacuum invariant under all of them. Despite the appearance of negative norm states in this quantization scheme, the energy operator is positive in all physical states, and vanishes in the vacuum. * pejhan@zjut.edu.cn † gazeau@apc.in2p3.fr ‡ Anzhong-Wang@baylor.edu 1 Here, in order to make our discussion explicit, we have used the so-called conformal (global) coordinates,

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“…[23]). The simplicity of group averaging for the present model is in part due working in low dimensions, but has more to do with the presence of conformal symmetry.…”

Section: Discussionmentioning

confidence: 99%

“…More formal discussions of group averaging can be found in [20,21]. Other studies of de Sitter group averaging include [22,23].…”

Section: Introductionmentioning

confidence: 99%

Group averaging of massless scalar fields in 1 + 1 de Sitter

Marolf

Morrison

2009

Class. Quantum Grav.

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Perturbative gravity in global de Sitter space is subject to so-called linearization stability constraints: If they are to couple consistently to the gravitational field, quantum states must be invariant under the de Sitter isometries. While standard Fock spaces contain no de Sitter-invariant states apart from (possibly) the vacuum, a full Hilbert space of de Sitter-invariant quantum states can be constructed via group averaging techiniques. We re-examine the simple toy model of de Sitter group averaging given by the free 1+1 scalar field, expanding on an earlier analysis by Higuchi. Our purpose is twofold: to include the scalar zero-mode, and to explicitly count the number of de Sitter-invariant states as a function of an appropriately defined energy.

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Group averaging for de Sitter free fields

Cited by 34 publications

References 52 publications

The graviton propagator in de Donder gauge on de Sitter background

The graviton propagator in de Donder gauge on de Sitter background

Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime

Group averaging of massless scalar fields in 1 + 1 de Sitter

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