Wave relations
Mathematical Physics
2020-02-03 v2 Analysis of PDEs
Algebraic Topology
Differential Geometry
math.MP
Symplectic Geometry
Abstract
The wave equation (free boson) problem is studied from the viewpoint of the relations on the symplectic manifolds associated to the boundary induced by solutions. Unexpectedly there is still something to say on this simple, well-studied problem. In particular, boundaries which do not allow for a meaningful Hamiltonian evolution are not problematic from the viewpoint of relations. In the two-dimensional Minkowski case, these relations are shown to be Lagrangian. This result is then extended to a wide class of metrics and is conjectured to be true also in higher dimensions for nice enough metrics. A counterexample where the relation is not Lagrangian is provided by the Misner space.
Cite
@article{arxiv.1308.5592,
title = {Wave relations},
author = {Alberto S. Cattaneo and Pavel Mnev},
journal= {arXiv preprint arXiv:1308.5592},
year = {2020}
}
Comments
27 pages; minor clarifying changes added; to appear in CMP