Green-Hyperbolic Operators on Globally Hyperbolic Spacetimes

2013/10/31 by Christian Baer, Christian Bär · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Bundle #Class (philosophy) #Differential (mechanical device) #Differential operator #Fourier integral operator #Geometric Analysis and Curvature Flows #Manifold (fluid mechanics) #Microlocal analysis #Operator theory #Stability and Controllability of Differential Equations #Vector bundle #math-ph #math.AP #math.DG #math.MP #msc:35L45 #msc:35L51 #msc:35L55 #msc:58J45 #msc:81T20

paper · pdf · doi:10.1007/s00220-014-2097-7

published as Commun. Math. Phys. 333, 1585-1615 (2015) · final version, suggestions by referee incorporated; the final publication is available at link.springer.com

openalex publication_date 2014/07/09 · arxiv created 2014/07/14 · arxiv updated 2015/01/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Green-hyperbolic operators are linear differential operators acting on sections of a vector bundle over a Lorentzian manifold which possess advanced and retarded Green's operators. The most prominent examples are wave operators and Dirac-type operators. This paper is devoted to a systematic study of this class of differential operators. For instance, we show that this class is closed under taking restrictions to suitable subregions of the manifold, under composition, under taking "square roots", and under the direct sum construction. Symmetric hyperbolic systems are studied in detail.

Citations

• The Large Scale Structure of Space-Time
• Hyperbolic Systems and Propagation on Causal Manifolds
• Symmetric hyperbolic systems for a large class of fields in arbitrary dimension

Cited by

• Poisson bracket and L_∞ algebras
• On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime
• On the global “two-sided” characteristic Cauchy problem for linear wave equations on manifolds