arXiv 0704.08412007-04hep-th

2- 4维四费米子相互作用模型中真空中的差费米子凝聚

Difermion condensates in vacuum in 2-4D four-fermion interaction models

Bang-Rong Zhou

备注：: 11 pages, 4 figures, General Poster 76 (Physical sciences) at 2007 AAAS Annual Meeting, San Francisco, Feb. 14-20, 2007, minor typos corrected,acknowledgment to financial supporter added

摘要：

真空中凝聚体$<\bar{q}q>$和$<qq>$之间相互作用的理论分析，一般是在二维、三维和四维的平均场近似下，用相对论有效势和双味和$N_c$色无质量费米子模型进行的。结果表明，在这些模型的基态，两种凝聚体之间的相互作用主要取决于$G_S/H_S$（2D和4D情况）或$G_S/H_P$（3D情况）的比值，其中$G_S$、$H_S$和$H_P$分别是标量$(\bar{q}q)$、标量$(qq)$和赝标量$(qq)$通道中的耦合常数.在所有模型的基态下，当$G_S/H_S$或$G_S/H_P$大于临界值$2/N_c$（进入凝聚体的费米子色数之比）时，只有纯的$<qq>$凝聚体存在.随着$G_S/H_S$或$G_S/H_P$减小到低于$2/N_c$的区域，模型的差异将显现出来。根据不同的模型，以及三维模型中的$N_c$，除了纯的$<qq>$冷凝物相之外，还将具有或不具有两种冷凝物的共存相。给出了这些模型中的$G_S-H_S$（或$G_S-H_P$）相图。结果还暗示了对双味类QCD NJL模型的一个实约束。

英文摘要：

Theoretical analysis of interplay between the condensates $<\bar{q}q>$ and $<qq>$ in vacuum is generally made by relativistic effective potentials in the mean field approximation in 2D, 3D and 4D models with two flavor and $N_c$ color massless fermions. It is found that in ground states of these models, interplay between the two condensates mainly depend on the ratio $G_S/H_S$ for 2D and 4D case or $G_S/H_P$ for 3D case, where $G_S$, $H_S$ and $H_P$ are respectively the coupling constants in a scalar $(\bar{q}q)$, a scalar $(qq)$ and a pseudoscalar $(qq)$ channel. In ground states of all the models, only pure $<\bar{q}q>$ condensates could exist if $G_S/H_S$ or $G_S/H_P$ is bigger than the critical value $2/N_c$, the ratio of the color numbers of the fermions entering into the condensates $<qq>$ and $<\bar{q}q>$. As $G_S/H_S$ or $G_S/H_P$ decreases to the region below $2/N_c$, differences of the models will manifest themselves. Depending on different models, and also on $N_c$ in 3D model, one will have or have no the coexistence phase of the two condensates, besides the pure $<qq>$ condensate phase. The $G_S-H_S$ (or $G_S-H_P$) phase diagrams in these models are given. The results also implicate a real constraint on two-flavor QCD-analogous NJL model.

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摘要：

英文摘要：

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