Topological Aspects of Quantum Field Theories

我们从两种不同的角度研究了“量子场论的拓扑方面”：一种是拓扑非平凡流形的量子力学研究，另一种是量子场论中拓扑非平凡手性孤子的研究。在流形上的量子力学研究中，我们证明了在2n维球面上出现的规范结构是广义BPST实例的规范结构。这表明在适当流形上研究量子力学可以得到非阿贝尔规范场理论的自对偶解。在对QCD中手性孤子（重子）的研究中，我们在1/N_C展开方案中得到了自旋翻转和自旋非翻转重子顶点的F/D比的显式N_C依赖关系，这使我们能够提取出N_C=3时重子的各种性质。

We have studied "Topologocal aspects of quantum field theories" from two different approaches : One is the study of quantum mechanics on the topologically non-trivial manifolds and another is the study of the topologically non-trivial chiral solitons in quantum field theory.In the study of quantum mechanics on manifolds we have shown that the gauge structure emerging on the 2n-dimensional sphere is that of the generalized BPST instantons. This shows that the self dual solutions of the non-abelian gauge field theory can be obtained by studying quantum mechanics on the apropriate manifold.In the study of chiral solitons (baryons) in QCD we have obtained in the 1/N_C expansion scheme, an explicit N_C dependences of the F/D ratios for both spin-flip and spin-nonflip baryon vertices, which enables us to extract various properties of baryons for N_C=3.