Analytic vectors, anomalies and star representations
The paper starts by reviewing the notion of analytic vectors and local representations of Lie algebras (i.e. non-integrable to the Lie group). The authors show in simple examples (one is the Heisenberg algebra acting on the space of square integrable functions on the circle) that local representations are in fact anomalous representations due to the lack of common analytic vectors which is produced by the topological nontriviality of its phase-space. To avoid these anomalies they propose to use a quantization which exploits the geometry of phase-space, e.g. star-quantization, which means a deformation of the algebra of observables in phase-space (a new - in general noncommutative - product law between functions in phase-space is introduced). In the above example this means replacing the Heisenberg algebra by the Euclidean algebra. They finally apply these ideas to simple two-dimensional field-theoretical models.
scientific article; zbMATH DE number 4132481