The project  Horizons  (ANR-16-CE40-0012-01) is funded by the Young Researcher (Jeunes Chercheuses et Jeunes Chercheurs)  programme of the ANR.

It runs from December 2016 to November 2019. The main host institution is the Institut Fourier.

Abstract of the project

The main topic is the application of techniques of asymptotic and global analysis to Quantum Field Theory on curved spacetimes and General Relativity, with the goal of studying quantum phenomena near and beyond spacetime horizons.

Striking physical phenomena are indeed believed to occur in setups where global and asymptotic aspects enter, geometrically often indicated by the presence of a horizon. Presently, conjectures regarding Hawking radiation, existence of the Hartle-Hawking and Unruh states on black hole spacetimes, or AdS-CFT duality remain unsolved due to significant gaps in our understanding of how the asymptotic analysis of hyperbolic differential equations relates to eg. propagation of singularities. The core idea is to implement a mixture of recently developed techniques from eg. asymptotic and microlocal analysis, as well as scattering and index theory to investigate and extend QFT to new curved backgrounds. Ultimately, the project seeks to explore extensions of quantum fields across spacetime horizons.

Members

Activities and events

Seminars

Workgroup seminar General Relativity and QFT, Institut Fourier, Grenoble

Meetings and conferences

Quantum fields, scattering and spacetime horizons: mathematical challenges,                Les Houches, 22-25 May 2018 

Mini lecture series

Christian Gérard (Paris-Saclay), Quantum Field Theory on Curved Spacetimes ,  Institut Fourier, Grenoble, 2018    [ Lecture notes ]

Publications

Publications and preprints of the project

[1] M. Wrochna: „The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes", Letters in Mathematical Physics, 107 (12), 2291-2331, arXiv:1612.01203 (2017)
[2] D. Häfner, C. Huneau: „Instability of infinitely many stationary solutions of the SU(2) Yang-Mills fields on the exterior of the Schwarzschild black hole", arXiv:1612.06596 (2016)
[3] T. Daudé, N. Kamran, F. Nicoleau: „On the hidden mechanism behind non-uniqueness for the anisotropic Calderón problem with data on disjoint sets", arXiv:1510.06559 (2016)
[4] C. Gérard, O. Oulghazi, M. Wrochna „Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry”, Communications in Mathematical Physics, 352 (2), 519-583, arXiv:1602.00930 (2017)
[5] C. Brouder, N. V. Dang, C. Laurent-Gengoux, K. Rejzner: „Properties of field functionals and characterization of local functionals", arXiv:1705.01937 (2017)
[6] C. Gérard, M. Wrochna: „Analytic Hadamard states, Calderón projectors and Wick rotation near analytic Cauchy surfaces", arXiv:1609.00192 (2017)
[7] M. Wrochna: „Conformal extension of the Bunch-Davies state across the de Sitter boundary", arXiv:1711.04011 (2017)
[8] T. Daudé, F. Nicoleau: „Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes", Mem. Amer. Math. Soc. 247, no. 1170, iv+113 pp., arXiv:1307.2842 (2017)
[9] C. Huneau, J. Luk: „High-frequency backreaction for the Einstein equations under polarized U(1) symmetry", arXiv:1706.09501 (2017)
[9] C. Huneau, J. Luk: „Einstein equations under polarized U(1) symmetry in an elliptic gauge", arXiv:1706.09499 (2017)
[10] N.V. Dang, B. Zhang: „Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-ups", arXiv:1712.03490 (2017)