| Abstract: | Locality, symmetry, infinite-dimensional groups, and exotic possibilities in quantum mechanics Local current algebras and groups embody the twin physical ideas of locality and symmetry. Because they are infinite-dimensional, many of the nice mathematical properties of the symmetry groups with which we are most familiar do not hold for them. Nevertheless they are conceptually beautiful objects, and their representations provide a unified description of a wide variety of quantum systems. In this talk, I shall describe how some exotic possibilities in quantum mechanics have been predicted from the study of unitary representations of groups of diffeomorphisms of physical space, and the corresponding Lie algebra of currents. These possibilities include "anyonic" or intermediate quantum statistics, and analogous possibilities for quantum theories of extended objects in 3-dimensional space, as well as certain possible modifications of quantum mechanics that admit nonlinearity and may describe dissipative systems. |
