Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

Fröb, Markus B.; Higuchi, Atsushi

doi:10.1063/1.4879496

Cited by 27 publications

(51 citation statements)

References 40 publications

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“…We next describe this procedure of subtracting the IRdivergent constant in terms of mode expansion of the propagator. We discuss it in any spacetime with the metric of the form (71) with N = 1. To start with we write down the Feynman propagator for the FP ghosts with M = 0 in terms of mode functions.…”

Section: Equivalence With the Faizal-higuchi Proposalmentioning

confidence: 99%

“…(F8) by explicit integration over the space using the two-point function found in Appendix C of Ref. [71].…”

Section: Appendix E: the Flat-torus Casementioning

confidence: 99%

“…In the rest of this appendix we show that Eq. (F8) results from the known two-point functions for the massless vector field in the literature [35,[69][70][71] as a consistency check.…”

mentioning

confidence: 99%

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Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections

Gibbons

Higuchi

2015

Phys. Rev. D

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It is well known that in de Sitter space the (free) minimally coupled massless scalar field theory does not admit any de Sitter-invariant Hadamard state. Related to this is the fact that the propagator for the massive scalar field corresponding to the de Sitter-invariant vacuum state diverges in the massless limit, with the infrared-divergent term being a constant. Since the Faddeev-Popov ghosts for the covariantly quantized Yang-Mills theory are minimally coupled massless scalar fields, it might appear that de Sitter symmetry would be broken in the ghost sector of Yang-Mills theory in de Sitter space. It is shown in this paper that the modes responsible for de Sitter symmetry breaking can be removed in a way consistent with BRST invariance and that a de Sitter-invariant theory can be constructed. More generally, it is shown that the spatially constant modes (the zero modes) of the Faddeev-Popov ghosts can be disposed of in a wide class of spacetimes with compact spatial sections. Then, the effective theory obtained by removing the zero modes, which contains a nonlocal interaction term, is shown to be equivalent to the theory corresponding to using a FaddeevPopov-ghost propagator with the constant infrared-divergent term removed, provided that one can freely integrate by parts in the spacetime integral at the vertex for the ghost interaction term.

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Section: Equivalence With the Faizal-higuchi Proposalmentioning

confidence: 99%

“…(F8) by explicit integration over the space using the two-point function found in Appendix C of Ref. [71].…”

Section: Appendix E: the Flat-torus Casementioning

confidence: 99%

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Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections

Gibbons

Higuchi

2015

Phys. Rev. D

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“…The "2c" contributions derive from making the following replacements in expressions (77)(78)(79)(80),…”

Section: Nonlocal De Sitter Breaking 3-3 Contributionsmentioning

confidence: 99%

Graviton loop corrections to vacuum polarization in de Sitter in a general covariant gauge

Glavan

Miao

Prokopec

et al. 2015

Class. Quantum Grav.

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We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations.

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“…The contribution of the l = 0 term in (3.16) to the function (3.15) corresponds to the correlator in dS spacetime in the absence of the cosmic string (for the two-point functions of vector fields, including the massive ones; see [42][43][44][45][46][47][48]). It is simplified to 20) where | x| 2 = r 2 + r 2 − 2rr cos φ + | z| 2 is the square of the spatial distance between the points x and x and we have defined the dS invariant quantity…”

Section: Two-point Functionsmentioning

confidence: 99%

Electromagnetic vacuum fluctuations around a cosmic string in de Sitter spacetime

2017

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The electromagnetic field correlators are evaluated around a cosmic string in background of (D + 1)-dimensional dS spacetime assuming that the field is prepared in the Bunch-Davies vacuum state. The correlators are presented in the decomposed form where the string-induced topological parts are explicitly extracted. With this decomposition, the renormalization of the local vacuum expectation values (VEVs) in the coincidence limit is reduced to the one for dS spacetime in the absence of the cosmic string. The VEVs of the squared electric and magnetic fields, and of the vacuum energy density are investigated. Near the string they are dominated by the topological contributions and the effects induced by the background gravitational field are small. In this region, the leading terms in the topological contributions are obtained from the corresponding VEVs for a string on the Minkowski bulk multiplying by the conformal factor. At distances from the string larger than the curvature radius of the background geometry, the pure dS parts in the VEVs dominate. In this region, for spatial dimensions D > 3, the influence of the gravitational field on the topological contributions is crucial and the corresponding behavior is essentially different from that for a cosmic string on the Minkowski bulk. There are well-motivated inflationary models which produce cosmic strings. We argue that, as a consequence of the quantum-to-classical transition of super-Hubble electromagnetic fluctuations during inflation, in the post-inflationary era these strings will be surrounded by large-scale stochastic magnetic fields. These fields could be among the distinctive features of the cosmic strings produced during the inflation and also of the corresponding inflationary models.

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Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

Cited by 27 publications

References 40 publications

Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections

Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections

Graviton loop corrections to vacuum polarization in de Sitter in a general covariant gauge

Electromagnetic vacuum fluctuations around a cosmic string in de Sitter spacetime

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