Quantization on manifolds and induced gauge potentials (Q2739430)

The author studies a system constrained on the \(D\)-dimensional sphere \(S^D\), using a generalization of the canonical commutation relations. To this aim a fundamental algebra is introduced, which stipulates operators of the system, and all its possible irreducible representations are determined by applying the induced representation technique. In quantizing the systems it is observed that a certain kind of gauge potential emerges. Furthermore, the relation of the presented approach to the Dirac formalism for a system constrained on \(S^D\) is examined, and comments are made on quantization for systems constrained on manifolds of different type.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00043].