论文标题
通过自发对称性破坏对Wigner-Eckart关系的校正
Corrections to Wigner-Eckart Relations by Spontaneous Symmetry Breaking
论文作者
论文摘要
操作员的矩阵元素转变为不间断的对称群体$ g $的不可约的表示，受众所周知的wigner-eckart关系的约束。对于无限扩展的系统，$ g $自发断裂，我们证明对这种关系的校正是由对称性破坏病房身份提供的，并且简单地减少到涉及金石玻色子的tadpole术语。该分析扩展到在哈密顿量中存在明确的对称性破坏项的情况，现在涉及伪金石玻色子的Tadpole术语。讨论了一个明确的例子，说明了这两种情况。
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.
