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Looking at Quantum Phenomena in terms of "Classical Glasses" -Analysis of Quantum (Field) Theory by means of Path Integration-

用“经典眼镜”看量子现象 -通过路径积分分析量子（场）理论-

基本信息

批准号：
12640280
负责人：
KASHIWA Taro
金额：
$ 2.3万
依托单位：
Ehime University (2002)Kyushu University (2000-2001)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

In the first two years, we have investigated the Nambu-Lona-Lasinio(NJL) model coupled to non-abelian gauge fields with non-zero background classical components. Introducing auxiliary fields and integrating fermi fields, we analize the effective action with being included quantum effects of non-abelian gauge fields. The calculations are nothing but those of two-loop orders so are very cumbersome. We have obtained results that (1) quantum effects of gauge fields enhance chiral symmetry breaking(χsb) , (2) dependence of the background magnetic fields to the dynamical mass is monotonically increasing in 4-dimension while in 3-dimension it is monotonically increasing in a region where χsb is small but decreasing where χsb is large. In the second and final years, we proceed to a more thorough investigation for the role of auxiliary fields in 4-fermi systems : inclusion of quantum effects of auxiliary fields to the gap equation in NJL to find that χsb is enhanced, justifying the auxiliary fields method. We also check that the higher order of auxiliary fields always improves results in 0-dimensional 4-fermi system (the Grassmann integration model) in which we encounter the case that the second derivative of the action vanishes at the saddle point, that is, of caustic.

在前两年中，我们研究了与具有非零背景经典分量的非阿贝尔规范场耦合的 Nambu-Lona-Lasinio（NJL）模型。引入辅助场并积分费米场，分析了包含非阿贝尔规范场量子效应的有效作用。计算只不过是两环阶的计算，非常麻烦。我们得到的结果是：（1）规范场的量子效应增强了手性对称性破缺（χsb），（2）背景磁场对动态质量的依赖性在 4 维中单调递增，而在 3 维中，在 χsb 小的区域单调递增，在 χsb 大的区域单调递减。在第二年和最后一年，我们对辅助场在 4-费米系统中的作用进行了更彻底的研究：将辅助场的量子效应纳入 NJL 中的能隙方程中，发现 χsb 得到了增强，从而证明了辅助场方法的合理性。我们还检查了辅助场的高阶总是会改善 0 维 4-费米系统（格拉斯曼积分模型）中的结果，其中我们遇到了作用的二阶导数在鞍点（即焦散）处消失的情况。