Abstract
It is known that there are no scalar Lie fields in more than two space-time dimensions [4]. Bilocal fields, however, which naturally arise in conformal operator product expansions, do generate infinite Lie algebras. Recent work, [2, 3], is reviewed, in which we classify such algebras and their unitary positive energy representations in a theory of a system of scalar fields of dimension two. The results are linked to the Doplicher–Haag–Roberts theory of superselection sectors governed by a (global) compact gauge group.
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