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Covariant pre-quantum operators

Josef Janyška, Marco Modugno

Published Jan 1, 2002• 3 citations
OpenAlex

Abstract

We study distinguished operators in the covariant formulation
of Quantum Machanics over a curved spacetime with absolute
time. Moreover, we classify all second-order covariant
operators on the quantum bundle.

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This paper concerns the quantization 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 quantize 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 wavefunctions on SO (3) in terms of single-valued sections of a new non-trivial quantum bundle. These results have clear analogies with spin.