论文标题
在NAMBU-JONA-LASINIO模型内磁场中pion质量的量规独立性
Gauge independence of pion masses in a magnetic field within the Nambu--Jona-Lasinio model
论文作者
论文摘要
我们研究了在恒定背景磁场中中性和带电亲的性能，主要是在nambu-jona-lasinio模型内零温度下。在先前的计算中，在动量空间随机相近似（RPA）〜[Phys。 Lett。 b $ \ textbf {782} $，155-161（2018）]。但是，尚未检查被带电的pion块的规格不变性。在这项工作中，通过基于假想时间路径积分形式主义采用线性响应理论，我们得出了在坐标空间中培养液位的相关函数，在该空间中，相应的schwinger阶段自动显示。在足够大的假想时间$τ$上，梅森相关函数接近指数形式$ \ sim \ exp（-e _ {\ rm g}τ）$，其中$ e _ {\ rm g} $是单人状态的基础能量，并确定为梅森质量。此外，我们表明，带电的PION的质量是独立的，即独立于对磁场的矢量潜力的选择。实际上，我们还发现动量空间RPA等同于此处使用的假想时间方法。
We investigate the properties of neutral and charged pions in a constant background magnetic field mainly at zero temperature within the Nambu--Jona-Lasinio model. In the previous calculations, the Ritus method, involving Schwinger phases in a fixed gauge, was employed within the momentum-space random phase approximation (RPA)~[Phys. Lett. B $\textbf{782}$, 155-161 (2018)]. However, gauge invariance of the charged pion masses has not yet been examined. In this work, by adopting the linear response theory based on the imaginary-time path integral formalism, we derive the correlation functions for pions in the coordinate space, where the corresponding Schwinger phases show up automatically. At sufficiently large imaginary time $τ$, the meson correlation function approaches an exponential form $\sim\exp(-E_{\rm G}τ)$, where $E_{\rm G}$ is the ground-state energy of the one-meson state and hence determined as the meson mass. Furthermore, we show that the mass of the charged pions is gauge independent, i.e., independent of the choice of the vector potential for the magnetic field. Actually, we also find that the momentum-space RPA is equivalent to the imaginary-time method used here.
