非相对论系统的有效拉格朗日量
Effective Lagrangian for Nonrelativistic Systems
摘要：
不具有Lorentz不变性的Nambu-Goldstone玻色子（NGB）的有效拉格朗日量具有一个新的特点，即部分NGB相互正则共轭，从而用两个NGB场描述$1$的动力学自由度.我们开发的显式形式，其有效的拉格朗日到二次阶导数。我们阐明了NGB自由度的计数规则，并基于陪集空间的拓扑结构对这种正则共轭对的可能性进行了完全分类。阐明了它对NGBs色散关系的影响。我们还提出了简单的缩放参数，看看NGB之间的相互作用是边缘或无关紧要的，这证明了在文献中关于对称性破缺的可能性在$1+1$尺寸的传说。
英文摘要：
The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing $1$ dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in $1+1$ dimensions.
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