A Unique Continuation Result for Klein-Gordon Bisolutions on a 2-dimensional Cylinder
arXiv:gr-qc/9804011 · doi:10.1088/0264-9381/16/3/011
Abstract
We prove a novel unique continuation result for weak bisolutions to the massive Klein-Gordon equation on a 2-dimensional cylinder M. Namely, if such a bisolution vanishes in a neighbourhood of a `sufficiently large' portion of a 2-dimensional surface lying parallel to the diagonal in the product manifold of M with itself, then it is (globally) translationally invariant. The proof makes use of methods drawn from Beurling's theory of interpolation. An application of our result to quantum field theory on 2-dimensional cylinder spacetimes will appear elsewhere.
LaTeX2e, 9 pages