Conformal Transformations as Observables

Details Conformal Transformations as Observables Conformal Transformations as Observables

2002-01-08

arxiv.org/abs/math-ph/0201016v3

Lett.Math.Phys.61:187-198,2002

Physics

Mathematical Physics

13 pages, no figures; analysis now covers conformal group of Minkowski space, minor additions, some typos corrected

Scientific paper

10.1023/A:1021242204872

C denotes either the conformal group in 3+1 dimensions, or in one chiral dimension. Let U be a unitary, strongly continuous representation of C satisfying the spectrum condition and inducing, by its adjoint action, automorphisms of a v.Neumann algebra A. We construct the unique inner representation U^A of the universal covering group of C implementing these automorphisms. U^A satisfies the spectrum condition and acts trivially on any U-invariant vector. This means in particular: Conformal transformations of a field theory having positive energy are weak limit points of local observables. Some immediate implications for chiral subnets are given. We propose the name ``Borchers-Sugawara construction''.

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