标题： 自旋泡沫微扰理论 显示英文标题

标题： Spin Foam Perturbation Theory

摘要： 我们研究在三角化流形上的自旋泡沫模型的摄动理论。 从这种类型的任何模型开始，我们考虑顶点幅度的任意摄动，并将摄动模型的演化算子写成控制摄动的耦合常数的收敛幂级数。 当未受摄动的模型是一个拓扑量子场论时，幂级数中的项可以高效计算。 此外，在这种情况下，当高维单形的数量趋于无穷大而耦合常数适当重正化时，我们可以显式地求和整个幂级数。 这个“稀薄气体极限”给出了与三角化无关但不是拓扑量子场论的自旋泡沫模型。 然而，我们证明这种类型的模型除了在二维之外都是相当平凡的。 显示英文摘要

摘要： We study perturbation theory for spin foam models on triangulated manifolds. Starting with any model of this sort, we consider an arbitrary perturbation of the vertex amplitudes, and write the evolution operators of the perturbed model as convergent power series in the coupling constant governing the perturbation. The terms in the power series can be efficiently computed when the unperturbed model is a topological quantum field theory. Moreover, in this case we can explicitly sum the whole power series in the limit where the number of top-dimensional simplices goes to infinity while the coupling constant is suitably renormalized. This `dilute gas limit' gives spin foam models that are triangulation-independent but not topological quantum field theories. However, we show that models of this sort are rather trivial except in dimension 2.