标题： 量子四面体和单纯自旋网络 显示英文标题

标题： Quantum tetrahedra and simplicial spin networks

摘要： 指出四面体与群SU(2)之间的一种新联系：将每个面与一个不可约的酉SU(2)表示相关联，并要求这些面闭合，则量子四面体的概念显现出来。 引入了量子四面体的希尔伯特空间，并表明由于不确定性关系，“四面体的几何”只能以“平均几何”的形式存在。 还提出了一种量子规范理论的动力学模型，该模型继承了环路表象方法在处理量子水平上的规范和微分不变性的优势，但完全基于组合学。 在这个模型中，量子四面体的概念找到了自然的应用，给出了用几何对象解释SU(2)自旋网络的可能性。 显示英文摘要

摘要： A new link between tetrahedra and the group SU(2) is pointed out: by associating to each face of a tetrahedron an irreducible unitary SU(2) representation and by imposing that the faces close, the concept of quantum tetrahedron is seen to emerge. The Hilbert space of the quantum tetrahedron is introduced and it is shown that, due to an uncertainty relation, the ``geometry of the tetrahedron'' exists only in the sense of ``mean geometry''. A kinematical model of quantum gauge theory is also proposed, which shares the advantages of the Loop Representation approach in handling in a simple way gauge- and diff-invariances at a quantum level, but is completely combinatorial. The concept of quantum tetrahedron finds a natural application in this model, giving a possible intepretation of SU(2) spin networks in terms of geometrical objects.