2009/03/05 by Ko Sanders · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-009-0900-7
published as Commun.Math.Phys.295:485-501,2010 · 18 pages
arxiv created 2009/03/05 · openalex publication_date 2009/08/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove that the singularity structure of all n -point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two-point distribution is of Hadamard form. In particular this applies to the free field and the result has applications in perturbative quantum field theory, showing that the class of all Hadamard states is the state space of interest. In our proof we assume that the field is a generalised free field, i.e. that it satisfies scalar (c-number) commutation relations, but it need not satisfy an equation of motion. The same arguments also work for anti-commutation relations and for vector-valued fields. To indicate the strengths and limitations of our assumption we also prove the analogues of a theorem by Borchers and Zimmermann on the self-adjointness of field operators and of a weak form of the Jost-Schroer theorem. The original proofs of these results make use of analytic continuation arguments. In our case no analyticity is assumed, but to some extent the scalar commutation relations can take its place.