QUANTUM REFERENCE FRAMES AND QUANTUM TRANSFORMATIONS

A quantum frame is defined by a material object following the laws of quantum mechanics. The present paper studies the relations between qua ntum frames, which are described by some generalization of the Poincar e group. The possibility of using a suitable quantum group is examined , but some arguments are given which show that a different mathematica l structure is necessary. Some simple examples in lower-dimensional sp ace-times are treated. They indicate the necessity of taking into acco unt some ''internal'' degrees of freedom of the quantum frames, that c an be disregarded in a classical treatment.