论文标题
（2+1）二维模型中的自发性非热性
Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
论文作者
论文摘要
使用Cornwall-Jackiw-Tomboulis有效的动作$γ（s）$用于复合操作员（$ s $是完整的费米昂传播器），在Harree-Fock（HF）近似值中研究了无质量（2 + 1）的相结构（2 + 1） - 尺寸较高的扭转模型。在这种情况下，整个费米昂繁殖器$ s $的$γ（s）$及其固定（或HF）方程都是按照裸耦合常数$ g $的一阶计算的。我们已经表明，在截止参数$λ$上，$ g \ equiv g（λ）$的依赖性明确定义，其hf方程被重新归一化。通常，它有两组（i）和（ii）的fermion传播溶液，与模型中不同质量项的动态外观相对应。在集合（i）的情况下，质量术语是冬宫，但是集合（ii）的解决方案对应于非弱点质量项的动态产生，即与毛刺模型的自发性非热性相对应。尽管如此，所有非铁基态的准粒子激发的质谱是真实的。此外，在这些非炎性阶段中，两个阶段都有$ \ cp \ ct $对称和非对称阶段。此外，与其他模型中对这种影响的先前研究相反，我们在{\ it sportive}（2+1）（2+1）二维模型中也观察到了自发的非热性现象。
Using the Cornwall-Jackiw-Tomboulis effective action $Γ(S)$ for composite operators ($S$ is the full fermion propagator), the phase structure of the massless (2 + 1)-dimensional Thirring model with four-component spinors is investigated in the Hartree-Fock (HF) approximation. In this case both $Γ(S)$ and its stationary (or HF) equation for the full fermion propagator $S$ are calculated in the first order of the bare coupling constant $G$. We have shown that there exist a well-defined dependence of $G\equiv G(Λ)$ on the cutoff parameter $Λ$ under which the HF equation is renormalized. In general, it has two sets, (i) and (ii), of solutions for fermion propagator corresponding to dynamical appearance of different mass terms in the model. In the case of set (i) the mass terms are Hermitian, but the solutions from the set (ii) correspond to a dynamical generation of the non-Hermitiam mass terms, i.e. to a spontaneous non-Hermiticity of the Thirring model. Despite this, the mass spectrum of the quasiparticle excitations of all non-Hermitian ground states is real. In addition, among these non-Hermitian phases there are both $\cP\cT$ symmetrical and non-symmetrical phases. Moreover, in contrast with previous investigations of this effect in other models, we have observed the spontaneous non-Hermiticity phenomenon also in the {\it massive} (2+1)-dimensional Thirring model.
