Wick rotation of linearized gravity in Gaussian time and Calder\'on projectors

Autor:	Gérard, Christian, Murro, Simone, Wrochna, Michał
Rok vydání:	2022
Předmět:	Mathematical Physics General Relativity and Quantum Cosmology Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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 Calder\'on 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. Comment: 63 pages; v2: substantial revision, corrects boundary terms in Sec. 6, introduction reworked
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.01094 Zobrazit plný text záznamu View this record from Arxiv