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Communications in Mathematical Physics

, Volume 332, Issue 3, pp 1083–1111 | Cite as

Wave Relations

  • Alberto S. CattaneoEmail author
  • Pavel Mnev
Article

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 about 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.

Keywords

Boundary Component Symplectic Structure Evolution Relation Hamiltonian Vector Wave Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZurichSwitzerland

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