大量子数展开中的若干问题
Selected Topics in the Large Quantum Number Expansion
摘要：
本文主要研究了在大电荷极限下具有整体对称性的量子场论和共形场论，并讨论了对称群的某些生成元。在低能量下，大电荷理论的部分由戈德斯通定理的混合形式描述，包括其相对论和非相对论形式。在红外线中的相关有效场论允许计算反常尺寸，和算子乘积展开系数在一个定义良好的全球电荷的逆幂展开。即使初始理论没有可靠的半经典近似，这也适用。大的量子数展开补充，并可能提供一种替代的方法的引导和数值处理。我们将介绍对称性破缺模式和低能有效作用量的一些一般特征，以及展示这种方法的显著特征的相当多的例子。
英文摘要：
In this review we study quantum field theories and conformal field theories with global symmetries in the limit of large charge for some of the generators of the symmetry group. At low energy the sectors of the theory with large charge are described by a hybrid form of Goldstone's theorem, involving its relativistic and non-relativistic forms. The associated effective field theory in the infrared allows the computation of anomalous dimensions, and operator product expansion coefficients in a well defined expansion in inverse powers of the global charge. This applies even when the initial theory does not have a reliable semiclassical approximation. The large quantum number expansion complements, and may provide an alternative approach to the bootstrap and numerical treatments. We will present some general features of the symmetry breaking patterns and the low-energy effective actions, and a fairly large number of examples exhibiting the salient features of this method.
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