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
Full Text:

References:

 [1] DOI: 10.1006/jfan.1996.3058 · Zbl 0964.46040 [2] DOI: 10.1063/1.522605 · Zbl 0316.46062 [3] DOI: 10.1007/BF02099011 · Zbl 0751.46045 [4] DOI: 10.1007/BF02096738 · Zbl 0809.46086 [5] DOI: 10.1142/S0129055X95000219 · Zbl 0836.46070 [6] DOI: 10.1007/BF02100053 · Zbl 0792.46052 [7] Buchholz D., Commun. Math. Phys. 155 pp 442– (1993) [8] DOI: 10.1007/BF01646454 [9] DOI: 10.1007/BF01388849 · Zbl 0691.22002 [10] DOI: 10.2307/1971477 · Zbl 0702.46044 [11] DOI: 10.1007/BF02097680 · Zbl 0734.46042 [12] DOI: 10.1007/BF02096548 · Zbl 0771.46039 [13] DOI: 10.1007/BF02101806 · Zbl 0831.46081 [14] DOI: 10.1007/BF02101672 · Zbl 0858.46053 [15] Guido D., Ann. Inst. Henri Poincaré 63 pp 383– (1995) [16] DOI: 10.1142/S0129167X93000054 · Zbl 0788.22005 [17] Isola T., J. Operator Theory 33 pp 3– (1995) [18] DOI: 10.1007/BF00750839 · Zbl 0836.46073 [19] DOI: 10.1023/A:1007300201901 · Zbl 0889.46059 [20] DOI: 10.1007/BF01236263 · Zbl 0513.43007 [21] DOI: 10.1016/0001-8708(74)90068-1 · Zbl 0284.46040 [22] DOI: 10.1007/BF01940769 · Zbl 0381.46034 [23] Summers S. J., Ann. Inst. Henri Poincaré 64 pp 409– (1996) [24] DOI: 10.1007/BF00750147 · Zbl 0807.47061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.