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

在前两年，我们研究了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，积分费米场，分析了包含量子效应的非阿贝尔规范场的有效作用。计算只是两个循环的订单，因此非常繁琐。结果表明：(1)规范场的量子效应增强了手征对称破缺(χ-SB)；(2)背景磁场对动力学质量的依赖在4维是单调增加的，而在3维是单调增加的，在χ-SB小的区域是单调增加的，而在χ-SB大的区域是单调增加的。在第二年和最后一年，我们继续对4-费米系统中辅助场的作用进行了更深入的研究：将辅助场的量子效应包含在NJL的能隙方程中，发现χSB得到了增强，证明了辅助场方法的合理性。我们还检验了在零维四费米系统(Grassmann积分模型)中，当我们遇到作用量的二阶导数在鞍点处消失，即焦散的情况时，高阶辅助场总是改善结果。

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.