Quantum Theory on Manifolds and its Application to Gauge Theory

流形的量子理论及其在规范理论中的应用

基本信息

批准号：
07804015
负责人：
TSUTSUI Izumi
金额：
$ 1.02万
依托单位：
University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

I considered quantization on a homogeneous space G/H as a first step toward quantizing on a manifold having a non-trivial topology. I showed that the inequivalent quantizations known to be allowed on the space G/H can be reproduced from the quantum theory on the group G by regarding the system as a constraint system and using Dirac's procedure applicable to such systems. I then showed that the induced gauge potential that appears on the space G/H is the canonical connection, and that it is essentially identical to the gauge potential which arises in the standard setting of Berry's phase. Next, as another class of models possessing a non-trivial manifold, I considered SL (n) Toda lattice models obtained by Hamiltonian reduction from the WZNW model. I classified all possible types of phases spaces obtained this way for n=2,3,4, and, in particular for the simplest case n=2, constructed the quantum theory explicitly where it is found that the theory is characterized by an angle parameter rheta.Quite independently of the above line of research, I also studied the path-integral approach to quantizing on G/H.I found that, by generalizing the approach for multiply-connected spaces, it is possible to recover the inequivalent quantizations if we add a weight factor given by irreducible representations of the subgroup H,and that this leads precisely to the system with the constraints mentioned above. Implication of this result to gauge theories is also examined in this path-integral framework.

我认为对均匀空间G/H的量化是量化具有非平凡拓扑的多种流形的第一步。我表明，可以通过将系统作为约束系统并使用适用于此类系统的DIRAC程序来从G/H上允许的不等量化量。然后，我表明，出现在空间g/h上的诱导的量规势是规范的连接，并且它与在贝瑞相位的标准环境中产生的量规势基本相同。接下来，作为另一类具有非平凡歧管的模型，我考虑了通过WZNW模型减少汉密尔顿（Hamiltonian）从WZNW模型中获得的SL（N）Toda晶格模型。 I classified all possible types of phases spaces obtained this way for n=2,3,4, and, in particular for the simplest case n=2, constructed the quantum theory explicitly where it is found that the theory is characterized by an angle parameter rheta.Quite independently of the above line of research, I also studied the path-integral approach to quantizing on G/H.I found that, by generalizing the approach for multiply-connected spaces, it is possible为了恢复不等的量化，如果我们添加亚组H不可还原表示给出的权重因子，并且这精确地导致了上述约束的系统。在此路径综合框架中还检查了该结果对衡量理论的影响。