关于双曲域上的Hubbard-Stratonovich变换
On Hubbard-Stratonovich Transformations over Hyperbolic Domains
摘要：
讨论并证明了双曲域上的Hubbard-Stratonovich（HS）恒等式在无序系统和随机矩阵研究中的有效性.我们还介绍了一个对应的HS身份出现在无序系统的“手征”对称性。除此之外，我们概述了从规范不变的Wegner $k-$轨道模型导出非线性$σ$模型的方法，避免了使用HS变换。
英文摘要：
We discuss and prove validity of the Hubbard-Stratonovich (HS) identities over hyperbolic domains which are used frequently in the studies on disordered systems and random matrices. We also introduce a counterpart of the HS identity arising in disordered systems with "chiral" symmetry. Apart from this we outline a way of deriving the nonlinear $σ$-model from the gauge-invariant Wegner $k-$orbital model avoiding the use of the HS transformations.
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