Lie group representations and quantization (Q5937875)

The authors investigate the representations of connected Lie groups on the basis of a group quantization formalism. The proposed technique is a generalization of the Kostant-Kirillov coadjoint orbits method for connected Lie groups and of the Borel-Weil-Bott representation algorithm for semisimple groups. The fundamentals of the group approach are applied to the simplest nontrivial example of the affine group in dimension one. The authors consider a simple nonanomalous example of the harmonic oscillator in the configuration space. Also, examples of infinite-dimensional anomalous groups are briefly considered.