#### The project

## 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

**Michał Wrochna**, Université Grenoble Alpes*(principal investigator)***Nguyen-Viet Dang**, Université Lyon 1**Thierry Daudé**, Université de Cergy-Pontoise**Dietrich Häfner**, Université Grenoble Alpes**Cécile Huneau**, Université Grenoble Alpes**Jean-Philippe Nicolas**, Université de Brest**Alexander Strohmaier**, University of Leeds

## 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) |