Remarks on the relation between causality and quantum fields. (English) Zbl 0804.53105
Quantum fields on curved spacetimes can be described in terms of nets of \(C^*\) algebras. It is interesting to inquire whether the corresponding net structure incorporates some information on the underlying spacetime geometry. The paper under consideration presents some interesting results on that score, concentrating on information on the causal structure of spacetimes. In particular, it is shown that a net isomorphism on a globally hyperbolic spacetime induces a conformal transformation of the underlying spacetime, provided that some technical conditions are satisfied. The case of a free Klein-Gordon field is treated in some detail.
Reviewer: V.Perlick (Berlin)
MSC:
81T05 | Axiomatic quantum field theory; operator algebras |
46L60 | Applications of selfadjoint operator algebras to physics |
53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
81T20 | Quantum field theory on curved space or space-time backgrounds |
83C47 | Methods of quantum field theory in general relativity and gravitational theory |