دانلود کتاب ساختار متریک کوانتومی SU(2) کوانتومی

Over the past century, the theory of operator algebras has given rise to an abundance of non-commutative analogues of classical mathematical theories, many of which have grown into successful independent research areas with exciting applications in theoretical physics. Prominent examples of this phenomenon include the theory of quantum groups [43, 79], non-commutative geometry à la Connes [14, 16–18], and Rieffel’s theory of quantum metric spaces [68, 70], which constitute far-reaching non-commutative generalisations of classical topological groups, Riemannian (spin) manifolds and compact metric spaces, respectively. Despite a continuous effort, it has proven very challenging to reconcile the theory of non-commutative geometry with the theory of quantum groups [19, 57], and even for the most fundamental qdeformation, Woronowicz’ SUq.2/, it is not clear how one should modify Connes’ axioms to obtain a non-commutative geometry which adequately reflects the underlying q-geometry. Numerous candidates for Dirac operators on SUq.2/ have been proposed [9, 13, 21, 38, 41, 42, 62], each having their advantages and disadvantages, but it seems unclear which (if any) of these provide SUq.2/ with the right kind of non-commutative geometry. At the time of writing, it is not even known if any of these Dirac operators give rise to a compact quantum metric structure, so also the connection between the metric geometry and the differential geometry on SUq.2/ is open.