Mathematics – Mathematical Physics
Scientific paper
Mar 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cmaph.100...57k&link_type=abstract
Communications in Mathematical Physics, Volume 100, Issue 1, pp.57-81
Mathematics
Mathematical Physics
41
Scientific paper
We consider the Klein-Gordon equation ( m≧0) on the double Schwarzschild wedge of the Kruskal spacetime, and construct the Hartle-Hawking state ω H as a thermal state relative to the Boulware quantization. We prove that, on the double wedge, ω H is a pure state, and in the corresponding representation, the left- and right-wedge C* algebras each have the Reeh-Schlieder property, while the corresponding von-Neumann algebras are type III 1 factors which are dual to (i.e. commutants of) each other. We discuss the extent to which these properties may generalize to non-quasi-free field theories. Pursuing the Rindler-Fulling-Unruh analogy with the Klein-Gordon equation ( m>0) in ( d-dimensional) flat spacetime, we establish an explicit formula for the Minkowski vacuum on a spacelike double wedge as a thermal state relative to the Fulling quantization. We also treat the case d=2, m=0 of this formula since this is essential input for a paper with Dimock on scattering theory for the quantum Klein-Gordon equation on the Schwarzschild metric.
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