论文标题
与对称性的量子场理论模型的退化扰动理论
Degenerate perturbation theory for models of quantum field theory with symmetries
论文作者
论文摘要
我们考虑了描述非相对论的玻色子相对论领域的非相对论量子力学物质的模型的哈密顿量。如果自由汉密尔顿人具有特征值，我们表明这种特征值也持续到非零耦合。自由汉密尔顿人的特征值可能会退化，只要存在一个对称群体，其对称性群体在特征空间不可否认。此外，如果哈密顿人在分析上取决于外部参数，那么特征值和特征向量也是如此。我们的结果适用于基态和共振状态。为了我们的结果，我们假设红外线状况是轻度的。该证明基于操作者理论重归于。它将[15]中使用的方法概括为非脱位情况，其中堕落者受对称群的保护，并利用Schur的诱饵来表达理论。
We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this eigenvalue persists also for nonzero coupling. The eigenvalue of the free Hamiltonian may be degenerate provided there exists a symmetry group acting irreducibly on the eigenspace. Furthermore, if the Hamiltonian depends analytically on external parameters then so does the eigenvalue and eigenvector. Our result applies to the ground state as well as resonance states. For our results we assume a mild infrared condition. The proof is based on operator theoretic renormalization. It generalizes the method used in [15] to non-degenerate situations, where the degeneracy is protected by a symmetry group, and utilizes Schur's lemma from representation theory.
