arXiv 2102.014912021-02-02hep-phhep-thmath-phmath.MPquant-ph

非厄米Nambu-Jona-Lasinio模型中的费米子和介子质量产生

Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models

Alexander Felski, S. P. Klevansky

备注：: 15 pages, 7 figures
发表信息：: Phys. Rev. D 103, 056007 (2021)
DOI：: 10.1103/PhysRevD.103.056007

摘要：

我们研究了非厄米性对相互作用费米子系统的影响。我们这样做，包括非厄米双线性项到3+1维Nambu-Jona-Lasinio（NJL）模型。两种可能的双线性修正产生了$\mathcal{PT}$对称理论;当标准NJL模型被伪矢量背景场$ig \barψγ_5 B_μγ^μψ$或反张量背景场$g \barψF_{μν}γ^μγ^νψ$扩展时，就会发生这种情况。剩下的三个双线性在性质上是{ \it反}- $\mathcal{PT}$ -对称的，即$ig \barψB_μγ^μψ, ig\barψγ_5 ψ$和$ig\barψ{1}ψ$，因此哈密顿算子没有整体对称性。此外，假载体$ig \barψγ_5 B_μγ^μψ$和载体$ig \barψB_μγ^μψ$组合是手性对称的。因此，在这个框架内，我们能够研究NJL模型的非厄米性、$\mathcal{PT}$对称性、手征对称性和两体相互作用的各种组合对真实有效费米子质量的存在和动力学产生的影响（这是相应的修改后的无质量自由狄拉克模型中不存在的特征）以及复合粒子的质量，赝标量和标量介子模式（$π$和$σ$介子）。我们的研究结果表明，$\mathcal{PT}$对称性是不必要的真正的费米子质量的解决方案存在，而是两体相互作用的NJL模型取代非厄米双线性效应。手征对称性的影响在介子模中最为明显，如果系统是手征对称的，那么介子模的赝标在本质上总是Goldstone。并讨论了介子方程的二阶解。

英文摘要：

We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model. Two possible bilinear modifications give rise to $\mathcal{PT}$ symmetric theories; this happens when the standard NJL model is extended either by a pseudovector background field $ig \barψγ_5 B_μγ^μψ$ or by an antisymmetric-tensor background field $g \barψF_{μν}γ^μγ^νψ$. The three remaining bilinears are {\it anti}-$\mathcal{PT}$-symmetric in nature, $ig \barψB_μγ^μψ, ig\barψγ_5 ψ$ and $ig\barψ{1}ψ$, so that the Hamiltonian then has no overall symmetry. The pseudovector $ig \barψγ_5 B_μγ^μψ$ and the vector $ig \barψB_μγ^μψ$ combinations, are, in addition, chirally symmetric. Thus, within this framework we are able to examine the effects that the various combinations of non-Hermiticity, $\mathcal{PT}$ symmetry, chiral symmetry and the two-body interactions of the NJL model have on the existence and dynamical generation of a real effective fermion mass (a feature which is absent in the corresponding modified massless free Dirac models) as well as on the masses of the composite particles, the pseudoscalar and scalar mesonic modes ($π$ and $σ$ mesons). Our findings demonstrate that $\mathcal{PT}$ symmetry is not necessary for real fermion mass solutions to exist, rather the two-body interactions of the NJL model supersede the non-Hermitian bilinear effects. The effects of chiral symmetry are evident most clearly in the meson modes, the pseudoscalar of which will always be Goldstone in nature if the system is chirally symmetric. Second solutions of the mesonic equations are also discussed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文