Physics – Mathematical Physics
Scientific paper
2006-04-27
Commun.Math.Phys.271:223-246,2007
Physics
Mathematical Physics
27 pages, v3: result improved by eliminating redundant assumption
Scientific paper
10.1007/s00220-006-0182-2
The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective gauge groups U(N) and O(N) confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory, but the approach using standard Lie algebra methods rather than abstract duality theory is complementary. The result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension D-2 in models with global conformal invariance. Another remarkable outcome is the observation that, with an appropriate choice of the Hamiltonian, a Lie algebra embedded into the associative algebra of observables completely fixes the representation theory.
Bakalov Bojko
Nikolov Nikolay
Rehren Karl-Henning
Todorov Ivan
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