SYMMETRIES IN THEORY OF LOCAL OBSERVABLES AND THE CHOICE OF THE NET OF LOCAL ALGEBRAS

Abstract

For a given net of algebras of local observables, satisfying standard assumptions, we propose the problem of classifying a net of subalgebras which provides the same physical consequences (possibly via Doplicher-Haag-Roberts sector theory) such as particle spectrum and scattering theory. The notion of symmetry of the net of local algebras are introduced and its geometrical aspects are analyzed, with the conclusion that the net reproduces the geometry of supporting regions to some extent. The internal symmetries provides a possible net of subalgebras, as is discussed by Doplicher, Haag and Roberts. We discuss other possibilities by generating subalgebras from a local observable. Results and problems for the simple case of a neutral massive scalar free Held are summarized.