非线性实现对称的Adler零拉格朗日量和有效拉格朗日量
Adler's Zero and Effective Lagrangians for Nonlinearly Realized Symmetry
摘要：
很久以前，Coleman，Callan，Wess和Zumino（CCWZ）通过寻找破缺群G的所有可能的非线性表示，当限制到未破缺群H时，这些非线性表示变成线性表示，构建了非线性实现对称的广义有效拉格朗日量。然而，在对应于破缺U（1）的单个南武-戈德斯通玻色子（NGB）的情况下，有效拉格朗日量也可以通过施加恒定的位移对称性来获得。在这项工作中，我们推广的移位对称的方法，以多个NGB和显示，当他们提供了一个线性表示的H，可以嵌入在一个对称陪集，它是可能的，以获得CCWZ拉格朗日施加1）“阿德勒的零条件”，这需要散射振幅消失时，发射一个单一的软NGB，和2）关闭的移位对称与线性实现的对称;完全不需要知道破群G。仅使用H的生成元，NGB协变导数和相关的规范场可以计算到NGB衰变常数f的所有阶。
英文摘要：
Long ago Coleman, Callan, Wess and Zumino (CCWZ) constructed the general effective lagrangian for nonlinearly realized symmetry by finding all possible nonlinear representations of the broken group G which become linear when restricted to the unbroken group H. However, in the case of a single Nambu-Goldstone boson (NGB), which corresponds to a broken U(1), the effective lagrangian can also be obtained by imposing a constant shift symmetry. In this work we generalize the shift symmetry approach to multiple NGBs and show that, when they furnish a linear representation of H that can be embedded in a symmetric coset, it is possible to derive the CCWZ lagrangian by imposing 1) the "Adler's zero condition," which requires scattering amplitudes to vanish when emitting a single soft NGB, and 2) closure of shift symmetry with the linearly realized symmetry; knowledge of the broken group G is not required at all. Using only generators of H, the NGB covariant derivative and the associated gauge field can be computed to all orders in the NGB decay constant f.
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