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

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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.