自发对称性破缺对Wigner-Eckart关系的修正
Corrections to Wigner-Eckart Relations by Spontaneous Symmetry Breaking
摘要：
变换为不破缺对称群$G$的不可约表示的算子的矩阵元由著名的Wigner-Eckart关系支配。在无限扩展系统的情况下，当$G$自发破缺时，我们证明了对这种关系的修正是由对称破缺沃德恒等式提供的，并简单地归结为一个包含Goldstone玻色子的蝌蚪项.分析延伸到一个明确的对称性破缺项存在于哈密顿量的情况下，与蝌蚪项现在涉及伪戈德斯通玻色子。一个明确的例子进行了讨论，说明了这两种情况。
英文摘要：
The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group $G$ are governed by the well-known Wigner-Eckart relations. In the case of infinitely-extended systems, with $G$ spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases.
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