论文标题
Nambu-Jona-lasinio模型的非热扩展在3+1和1+1维度
Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions
论文作者
论文摘要
本文介绍了在3+1和1+1尺寸中的Nambu-Jona-lasinio（NJL）模型的非热pt对称扩展。在3 + 1个维度中，su（2）-symmetric njl hamiltonian $ h _ {\ textrm {\ textrm {njl}} = \barψ（-iγ^k \ partial_k + partial_k + m_0）ψ- pt和手性 - 对称双线性项$ ig \barψγ_5b_μγ^μψ$;在1+1个维度中，其中$ h _ {\ textrm {njl}} $是Gross-Neveu模型的一种形式，它是由非热pt-对称性但chiral symmetry breaking term $ g \ g \ bar \ barψγ_5ψ$扩展的。在每种情况下，都会得出差距方程，并研究了非铁词术语对产生质量的影响。我们有几个发现：在以前的自由狄拉克方程进行的计算中，与预期相反，已修改以包含非热的双线性项，在手性极限中无法获得实际的质谱；在这些情况下，非零的裸质量质量对于实现不间断的PT对称性至关重要。在这里，在存在四点相互作用的NJL模型中，我们{\ IT}在3+1和1+1尺寸中消失的裸质量的极限也至少对于非高层couplings $ g $的某些特定值，也可以找到质谱的真实值。因此，四点相互作用覆盖了导致这些参数值的PT对称性破坏的效果。此外，我们发现，在这两种情况下，在3+1和1+1维中，包含非铁线双线性项可以有助于产生的质量。在这两个模型中，这种贡献都可以调节为小。因此，当$ m_0 = 0 $在没有非铁词项的情况下，我们将费米质量固定在其值时，然后确定所需的耦合值以生成裸露的质量质量。
This paper presents a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics in 3+1 and 1+1 dimensions. In 3+1 dimensions, the SU(2)-symmetric NJL Hamiltonian $H_{\textrm{NJL}} = \barψ(-i γ^k \partial_k + m_0) ψ- G [ (\barψψ)^2 + (\barψi γ_5 \vecτ ψ)^2 ]$ is extended by the non-Hermitian, PT- and chiral-symmetric bilinear term $ig\barψγ_5 B_μ γ^μ ψ$; in 1+1 dimensions, where $H_{\textrm{NJL}}$ is a form of the Gross-Neveu model, it is extended by the non-Hermitian PT-symmetric but chiral symmetry breaking term $g \barψγ_5 ψ$. In each case, the gap equation is derived and the effects of the non-Hermitian terms on the generated mass are studied. We have several findings: in previous calculations for the free Dirac equation modified to include non-Hermitian bilinear terms, contrary to expectation, no real mass spectrum can be obtained in the chiral limit; in these cases a nonzero bare fermion mass is essential for the realization of PT symmetry in the unbroken regime. Here, in the NJL model, in which four-point interactions are present, we {\it do} find real values for the mass spectrum also in the limit of vanishing bare masses in both 3+1 and 1+1 dimensions, at least for certain specific values of the non-Hermitian couplings $g$. Thus, the four-point interaction overrides the effects leading to PT symmetry-breaking for these parameter values. Further, we find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass. In both models, this contribution can be tuned to be small; we thus fix the fermion mass to its value when $m_0=0$ in the absence of the non-Hermitian term, and then determine the value of the coupling required so as to generate a bare fermion mass.
