Wick Rotation of Linearized Gravity in Gaussian Time and Calderón Projectors

Christian Gérard; Simone Murro; Michał Wrochna

doi:10.1007/s00023-025-01539-1

Wick Rotation of Linearized Gravity in Gaussian Time and Calderón Projectors

Christian Gérard, Simone Murro, Michał Wrochna^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Motivated by the quantization of linearized gravity, we consider gauge-fixed linearized Einstein equations and their Wick rotation near a Cauchy surface. We show that Calderón projectors for the Wick-rotated equations induce Hadamard bi-solutions on the Lorentzian level. On the other hand, we find smoothing obstructions to gauge-invariance and positivity conditions needed in quantization. These obstructions are primarily due to boundary terms arising in the Wick-rotated theory and depend on the boundary conditions.

Original language	English
Article number	082301
Journal	Annales Henri Poincare
DOIs	https://doi.org/10.1007/s00023-025-01539-1
Publication status	E-pub ahead of print - 20 Jan 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Funding

S.M. was supported by the DFG research grant MU 4559/1-1 "Hadamard States in Linearized Quantum Gravity". Support from the Grant ANR-20-CE40-0018 is gratefully acknowledged. The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk & lstrok;odowska-Curie Grant Agreement No 754340.

Funders	Funder number
Horizon 2020 Framework Programme
Deutsche Forschungsgemeinschaft	ANR-20-CE40-0018, MU 4559/1-1
H2020 Marie Skłodowska-Curie Actions	754340

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Cite this

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AB - Motivated by the quantization of linearized gravity, we consider gauge-fixed linearized Einstein equations and their Wick rotation near a Cauchy surface. We show that Calderón projectors for the Wick-rotated equations induce Hadamard bi-solutions on the Lorentzian level. On the other hand, we find smoothing obstructions to gauge-invariance and positivity conditions needed in quantization. These obstructions are primarily due to boundary terms arising in the Wick-rotated theory and depend on the boundary conditions.

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Wick Rotation of Linearized Gravity in Gaussian Time and Calderón Projectors

Abstract

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