Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is of the form F_1^G otimes I for a suitable decomposition F=F_1 otimes F_2 and a compact group action. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors.
Carpi, S., Conti, R. (2001). Classification of subsystems for local nets with trivial superselection structure. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 217(1), 89-106 [10.1007/PL00005550].
Classification of subsystems for local nets with trivial superselection structure
Carpi, S;
2001-01-01
Abstract
Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is of the form F_1^G otimes I for a suitable decomposition F=F_1 otimes F_2 and a compact group action. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors.| File | Dimensione | Formato | |
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