Topological Aspects of Quantum Field Theory.

以下是1997-1998年在“量子场论的拓扑方面”研究项目下完成的研究论文。1.N=1超对称规范规范理论中的负维群外推和对偶性。在本文中，我们将“负维群”的思想应用于“对偶”的研究。我们在N=1超对称SO(2N)和Sp(2N)规范理论中建立了有趣的对偶关系。2.二维孤子零模的诱导规范结构本文计算了1 1维sigma模型中的诱导规范结构，注意到孤子解的零模在拓扑上与量子力学相对应。非平凡流形。3. 3(N) 和 MERON 解的量子力学。研究了 3 维球体上的量子力学，发现诱导规范结构是“meron”的。4.SKYRME 模型中的不等价量子化。3 1 维 sigma 模型中“Skyrmion”的不等价量化被发现存在并给出不同的物理预测。

The followings are the research papers completed during the years 1997-1998 under the research project 'Topological Aspects of Quantum Field Theory'.1.NEGATIVE DIMENSIONAL GROUP EXTRAPOLATION AND DUALITY IN N=1 SUPERSYM-METRIC GAUGE THEORIES.in this paper we have applied the idea of 'negative dimensional groups' in the studies of 'duality' . We have established an interesting relation between the dualities in N=1 Supersymmetric SO(2N) and Sp(2N) Gauge Theories.2.INDUCED GAUGE STRUCTURE FOR THE ZERO MODES OF TWO DIMENSIONAL SOLITONS.In this paper we have calculated the induced gauge structure in 1+1 dimensional sigma model, noticing the fact that the zero mode of the soliton solution corres ponds to the quantum mechanics on the topologically nontrivial manifold.3.QUANTUM MECHANICS ON 3(N) AND MERON SOLUTION.Quantum Mechanics on the 3 dimensional sphere has been investigated and the induced gauge structure has been found to be that of 'meron'.4.INEQUIVALENT QUANTIZATION IN THE SKYRME MODEL.Inequivalent quantizations of the 'Skyrmion' in 3+1 dimensional sigma model have been found to exist andto give different physical predictions.