再论畴壁费米子的振荡行为
Oscillatory behavior of the domain wall fermions revisited
摘要：
在格点上手征费米子的一般畴壁费米子表述中，具有负质量参数$-M_5$的四维Wilson费米子算符的零模引入了非物理质量模在四维时空中传播.在自由费米子情况下，这类非物理模的极点质量由$\tilde{E}=\ln(1-M_5)$给出，当$M_5>1$时，它获得一个虚部$iπ$，导致畴壁费米子传播子随时间的振荡行为.在平均场近似下，研究了规范场存在时非物理模的存在性，并讨论了它们的物理后果。此外，我们还给出了一个半定量的准则，调整$M_5$在现实的数值研究。
英文摘要：
In the generic domain wall fermion formulation of chiral fermions on the lattice, the zero modes of the four-dimensional Wilson fermion operator with the negative mass parameter $-M_5$ introduce unphysical massive modes propagating in the four-dimensional spacetime. In the free fermion case, the pole mass of this kind of unphysical modes is given by $\tilde{E}=\ln(1-M_5)$, which acquires an imaginary part, $iπ$, when $M_5>1$ and results in an oscillatory behavior of the domain wall fermion propagator in time. The existence of the unphysical modes in the presence of gauge fields is investigated in the mean field approximation, and their physical consequences are discussed. In addition, we also give a semiquantitative criterion for tuning $M_5$ in the realistic numerical study.
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