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Extension of anti-automorphisms and PCT-symmetry. (English) Zbl 1044.81083

Summary: We study conditions for an anti-automorphism of a \(C^*\)-algebra to extend to the cross-product by a compact group dual action. As a byproduct, we show that under a few natural assumptions any PCT transformation \(q\) of \(A\), the observable net of a local QFT, extends to the canonical field net \(F\). Then we discuss the validity of ta certain relation for every DHR morphism \(r\) of \(A\) with finite statistics.

MSC:

81T05 Axiomatic quantum field theory; operator algebras
46L40 Automorphisms of selfadjoint operator algebras
46L60 Applications of selfadjoint operator algebras to physics
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