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.
A covariant approach to the quantisation of a rigid body / M. MODUGNO; C. TEJERO PRIETO; R. VITOLO. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - STAMPA. - 41:(2008), pp. 1-47. [10.1088/1751-8113/41/3/035304]
A covariant approach to the quantisation of a rigid body
MODUGNO, MARCO;
2008
Abstract
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.File | Dimensione | Formato | |
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