arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1009.2149hep-lathep-exhep-phnucl-exnucl-th
收藏

格点量子色动力学中的Wilson费米子行列式

Wilson Fermion Determinant in Lattice QCD

Keitaro Nagata, Atsushi Nakamura

摘要:

给出了一个将Wilson费米子的秩从$4 N_c N_x N_y N_z N_t$降到$4 N_c N_x N_y N_z$而保持其行列式值的公式。利用$4^4$格点上格点量子色动力学组态,分析了费米子行列式$\sum_n C_n (\exp(μ/T))^n$逸度展开中约化矩阵的本征值和系数$C_n$,它们在正则公式中起着重要作用.数值上,$\log |C_n|$随$N_x N_y N_z$变化,并且很容易超过标准数值范围;我们给出了一个简单的解决方法。$C_n$的相位与复杂平原中波利雅科夫环的分布相关。这些结果为今后格点量子色动力学的有限密度计算奠定了基础。

英文摘要:

We present a formula for reducing the rank of Wilson fermions from $4 N_c N_x N_y N_z N_t$ to $4 N_c N_x N_y N_z$ keeping the value of its determinant. We analyse eigenvalues of a reduced matrix and coefficients $C_n$ in the fugacity expansion of the fermion determinant $\sum_n C_n (\exp(μ/T))^n$, which play an important role in the canonical formulation, using lattice QCD configurations on a $4^4$ lattice. Numerically, $\log |C_n|$ varies as $N_x N_y N_z$, and goes easily over the standard numerical range; We give a simple cure for that. The phase of $C_n$ correlates with the distribution of the Polyakov loop in the complex plain. These results lay the groundwork for future finite density calculations in lattice QCD.

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。

↑