Finster, Felix and Much, Albert (2023) A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes. ANNALES HENRI POINCARE, 24 (4). pp. 1185-1209. ISSN 1424-0637, 1424-0661
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The bosonic signature operator is defined for Klein-Gordon fields and massless scalar fields on globally hyperbolic Lorentzian manifolds of infinite lifetime. The construction is based on an analysis of families of solutions of the Klein-Gordon equation with a varying mass parameter. It makes use of the so-called bosonic mass oscillation property which states that integrating over the mass parameter generates decay of the field at infinity. We derive a canonical decomposition of the solution space of the Klein-Gordon equation into two subspaces, independent of observers or the choice of coordinates. This decomposition endows the solution space with a canonical complex structure. It also gives rise to a distinguished quasi-free state. Taking a suitable limit where the mass tends to zero, we obtain corresponding results for massless fields. Our constructions and results are illustrated in the examples of Minkowski space and ultrastatic spacetimes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HADAMARD STATES; NONPERTURBATIVE CONSTRUCTION; SINGULARITY STRUCTURE; FERMIONIC PROJECTOR; 2-POINT FUNCTION; STATIONARY; TIMES |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 20 Feb 2024 10:46 |
| Last Modified: | 20 Feb 2024 10:46 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56928 |
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