Bisolutions to the KleinGordon equation and quantum field theory on twodimensional cylinder spacetimes
Abstract
We consider 2dimensional cylinder spacetimes whose metrics differ from the flat Minkowskian metric within a compact region. By choice of time orientation, these spacetimes may be regarded as either globally hyperbolic timelike cylinders or nonglobally hyperbolic spacelike cylinders. For generic metrics in our class, we classify all possible candidate quantum field algebras for massive KleinGordon theory which obey the Flocality condition introduced by Kay. This condition requires each point of spacetime to have an intrinsically globally hyperbolic neighbourhood, N, such that the commutator (in the candidate algebra) of fields smeared with test functions supported in N agrees with the value obtained in the usual construction of KleinGordon theory on N. By considering bisolutions to the KleinGordon equation, we prove that generic timelike cylinders admit a unique Flocal algebra  namely the algebra obtained by the usual construction  and that generic spacelike cylinders do not admit any Flocal algebras, and are therefore non Fquantum compatible. Refined versions of our results are obtained for subclasses of metrics invariant under a symmetry group. Thus Flocal field theory on 2dimensional cylinder spacetimes essentially coincides with the usual globally hyperbolic theory. In particular the result of the author and Higuchi that the Minkowskian spacelike cylinder admits infinitely many Flocal algebras is now seen to represent an anomalous case.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 March 1999
 DOI:
 10.1088/02649381/16/3/010
 arXiv:
 arXiv:grqc/9804012
 Bibcode:
 1999CQGra..16..769F
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 LaTeX2e, 25 pages