Classical Klein-Gordon solutions, symplectic structures and isometry actions on AdS spacetimes
arXiv:1212.2945 · doi:10.1016/j.geomphys.2013.03.007
Abstract
We study classical, real Klein-Gordon theory on Lorentzian Anti de Sitter (AdS_{1,d}) spacetimes with spatial dimension d. We give a complete list of well defined and bounded Klein-Gordon solutions for three types of regions on AdS: slice (time interval times all of space), rod hypercylinder (all of time times solid ball in space), and tube hypercylinder (all of time times solid shell in space). Hypercylinder regions are of natural interest for AdS since the neighborhood of the AdS-boundary is a tube. For the solution spaces of our regions we find the actions induced by the AdS isometry group SO(2,d). For all three regions we find one-to-one correspondences between initial data and solutions on the regions. For rod and tube regions this initial data can also be given on the AdS boundary. We calculate symplectic structures associated to the solution spaces, and show their invariance under the isometry actions. We compare our results to the corresponding expressions for (3+1)-dimensional Minkowski spacetime, arising from AdS_{1,3} in the limit of large curvature radius.
28 pages, RevTex 4.1
References in corpus (6)
- Spatially asymptotic S-matrix from general boundary formulation
- S-matrix at spatial infinity
- General boundary quantum field theory in de Sitter spacetime
- Configuration Space Methods and Time Ordering for Scalar Propagators in (Anti and) de Sitter Spacetimes
- Coordinate representation of particle dynamics in AdS and in generic static spacetimes
- Reverse Engineering Quantum Field Theory