Differential operators cononically associated to a conformal structure.

Branson, Thomas

doi:10.7146/math.scand.a-12120

Cited by 222 publications

(203 citation statements)

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“…3 See [48] for some discussion of higher derivative theories in flat space, [49,50] for some earlier discussion on conformal operators and [51][52][53][54] for selected math literature.…”

Section: Jhep06(2014)066mentioning

confidence: 99%

On conformal higher spin wave operators

Nutma

Taronna

2014

J. High Energ. Phys.

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We analyze free conformal higher spin actions and the corresponding wave operators in arbitrary even dimensions and backgrounds. We show that the wave operators do not factorize in general, and identify the Weyl tensor and its derivatives as the obstruction to factorization. We give a manifestly factorized form for them on (A)dS backgrounds for arbitrary spin and on Einstein backgrounds for spin 2. We are also able to fix the conformal wave operator in d = 4 for s = 3 up to linear order in the Riemann tensor on generic Bach-flat backgrounds.

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“…3 See [48] for some discussion of higher derivative theories in flat space, [49,50] for some earlier discussion on conformal operators and [51][52][53][54] for selected math literature.…”

Section: Jhep06(2014)066mentioning

confidence: 99%

On conformal higher spin wave operators

Nutma

Taronna

2014

J. High Energ. Phys.

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“…The Yamabe operator has conformai bidegree ((am -2)/2, (am + 2)/2). Somewhat less well-known is the fourth-order Paneitz operator P4 , which was introduced in [P] (see also [Bral,Theorem 1.21], and [ES]). To describe P, let p be the Ricci tensor of V ; py = Rk ¡kj , and let…”

Section: Conformally Covariant Differential Operators On Scalar Functmentioning

confidence: 99%

Sharp Inequalities, the Functional Determinant, and the Complementary Series

Branson¹

1995

Transactions of the American Mathematical Society

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146

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Abstract.Results in the spectral theory of differential operators, and recent results on conformally covariant differential operators and on sharp inequalities, are combined in a study of functional determinants of natural differential operators. The setting is that of compact Riemannian manifolds. We concentrate especially on the conformally flat case, and obtain formulas in dimensions 2, 4, and 6 for the functional determinants of operators which are well behaved under conformai change of metric. The two-dimensional formulas are due to Polyakov, and the four-dimensional formulas to Branson and Orsted; the method is sufficiently streamlined here that we are able to present the sixdimensional case for the first time. In particular, we solve the extremal problems for the functional determinants of the conformai Laplacian and of the square of the Dirac operator on S2 , and in the standard conformai classes on S4 and S6 . The S2 results are due to Onofri, and the S4 results to Branson, Chang, and Yang; the S6 results are presented for the first time here. Recent results of Graham, Jenne, Mason, and Sparling on conformally covariant differential operators, and of Beckner on sharp Sobolev and Moser-Trudinger type inequalities, are used in an essential way, as are a computation of the spectra of intertwining operators for the complementary series of SOo(m + 1, 1), and the precise dependence of all computations on the dimension. In the process of solving the extremal problem on S6 , we are forced to derive a new and delicate conformally covariant sharp inequality, essentially a covariant form of the Sobolev embedding L2(S6) «-» L3(S6) for section spaces of trace free symmetric two-tensors.

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“…All quantities with an overbar are evaluated in the fixed fiducial metricḡ µν . The fourth order differential operator [32,[41][42][43][44][45] …”

Section: The Conformal Anomaly and Low Energy Eft Of Gravitymentioning

confidence: 99%

Scalar gravitational waves in the effective theory of gravity

Mottola

2017

J. High Energ. Phys.

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As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective action associated with the trace anomaly is expressed in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. Linearized around flat spacetime, this semi-classical EFT admits scalar gravitational wave solutions in addition to the transversely polarized tensor waves of the classical Einstein theory. The amplitude of the scalar wave modes, as well as their energy and energy flux which are positive and contain a monopole moment, are computed. Astrophysical sources for scalar gravitational waves are considered, with the excited gluonic condensates in the interiors of neutron stars in merger events with other compact objects likely to provide the strongest burst signals.

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Differential operators cononically associated to a conformal structure.

Cited by 222 publications

References 0 publications

On conformal higher spin wave operators

On conformal higher spin wave operators

Sharp Inequalities, the Functional Determinant, and the Complementary Series

Scalar gravitational waves in the effective theory of gravity

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