Quantising a rigid body

Raffaele Vitolo

E-mail: vitolo@ilenic.unile.it

Abstract. This paper concerns the quantisation of a rigid body in the framework of the ``covariant quantisation'' on a curved spacetime with absolute time proposed by A. Jadczyk and M. Modugno. We start with a spacetime for a pattern one--body mechanics, which is constituted by a $4$--dimensional affine space fibred over time and equipped with a vertical Euclidean metric and an electromagnetic field. Then, we obtain the multi--spacetime for $n$--body mechanics by taking the $n$--fold fibred product of the above structure. Eventually, we obtain the spacetime for a rigid body by considering the fibred subbundle of the multi--spacetime defined by a rigid constraint. We show that the general scheme of the ``covariant quantisation'' can be easily applied to the rigid body. In particular, we are concerned with the existence and classification of the inequivalent quantum structures.

AMSclassification. 53C05, 53C15, 55N05, 55N30, 58A20, 58F06, 70H40, 70E99, 81S10

Keywords. Covariant quantisation, rigid body