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.
A covariant approach to the quantisation of a rigid body
VITOLO, Raffaele
2008-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
