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Analytic dependence is an unnecessary requirement in renormalization of locally covariant QFT. (English) Zbl 1351.81081
In their axioms for Wick powers in locally covariant quantum field theory on curved space-times [ibid. 223, No. 2, 289–326 (2001; Zbl 0989.81081)], S. Hollands and R. M. Wald required a certain analyticity of expectation values of Wick powers under analytic changes of analytic background data. This is somewhat unsatisfactory, as the framework is otherwise independent of any analyticity requirements and emphasizes the locality of all constructions.
The authors show that the analyticity requirement is indeed not a necessary requirement for the essential uniqueness of Wick powers. This provides an important simplification of the original axioms of Hollands & Wald. The proof relies on the Peetre-Slovák theorem.

MSC:
81T20 Quantum field theory on curved space or space-time backgrounds
81T05 Axiomatic quantum field theory; operator algebras
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