A covariant approach to the quantisation of a rigid body

N. 035304 - arXiv:math-ph/0511020 This paper concerns the quantisation of a rigid body in the framework of "covariant quantum mechanics" on a curved spacetime with absolute time. We consider the configuration space of n classical particles as the n-fold product of the configuration space of one particle. Then, we impose a rigid constraint and the resulting space is dealt with as a configuration space of a single abstract `particle'. This classical framework turns out to be suitable for the formulation of covariant quantum mechanics according to this scheme. Thus, we quantise such a `particle' accordingly. This scheme can model, e.g., the quantum dynamics of extremely cold molecules. We provide a new mathematical interpretation of two-valued wave functions on SO(3) in terms of single-valued sections of a new non-trivial quantum bundle. These results have clear analogies with spin. Key words: Covariant classical mechanics, covariant quantum mechanics, rigid body. MSC2000: 81S10,58A20,58C40,70G45,70E17,70H40,81Q10,81V55.