PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION

被引：11

作者：

Gannot, Oran ^{[1
]}

Wrochna, Michal ^{[2
]}

机构：

[1] Northwestern Univ, Dept Math, Lunt Hall, Evanston, IL 60208 USA

[2] Univ Cergy Pontoise, 2 Av Adolphe Chauvin, F-95302 Cergy Pontoise, France

来源：

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2022年 / 21卷 / 01期

关键词：

propagation of singularities; Klein-Gordon equation; anti-de Sitter spacetimes; quantum field theory on curved spacetimes; Hadamard states; MASSIVE WAVE-EQUATION; UNIQUE CONTINUATION; ELLIPTIC THEORY; INFINITY; MANIFOLDS; OPERATORS; METRICS;

D O I：

10.1017/S147474802000002X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Klein-Gordon equation on asymptotically anti-de-Sitter spacetimes subject to Neumann or Robin (or Dirichlet) boundary conditions and prove propagation of singularities along generalized broken bicharacteristics. The result is formulated in terms of conormal regularity relative to a twisted Sobolev space. We use this to show the uniqueness, modulo regularizing terms, of parametrices with prescribed b-wavefront set. Furthermore, in the context of quantum fields, we show a similar result for two-point functions satisfying a holographic Hadamard condition on the b-wavefront set.

引用

页码：67 / 127

页数：61

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