格点上的伽利略不变性恢复
Galilean invariance restoration on the lattice
摘要：
我们考虑了在移动标架中由于不同的格点截断效应而导致的伽利略不变性的破坏，以及在核格点相互作用的构造中所使用的非局部涂抹参数。利用色散关系和中子-质子散射相移研究了伽利略不变性的破坏效应和恢复方法，给出了用Lüscher公式和球壁方法计算的$S$波道、${}^1S_0$和${}^3S_1$的中子-质子散射相移和色散关系。对于$P$和$D$波，我们给出了用球壁方法计算的中子-质子散射相移。我们发现，伽利略不变性破坏的影响，源自晶格文物部分取消所造成的非局部涂抹参数。由于这种抵消，伽利略不变性破坏的影响很小，伽利略不变性可以通过引入伽利略不变性恢复算子来恢复。
英文摘要：
We consider the breaking of Galilean invariance due to different lattice cutoff effects in moving frames and a nonlocal smearing parameter which is used in the construction of the nuclear lattice interaction. The dispersion relation and neutron-proton scattering phase shifts are used to investigate the Galilean invariance breaking effects and ways to restore it. For $S$-wave channels, ${}^1S_0$ and ${}^3S_1$, we present the neutron-proton scattering phase shifts in moving frames calculated using both Lüscher's formula and the spherical wall method, as well as the dispersion relation. For the $P$ and $D$ waves, we present the neutron-proton scattering phase shifts in moving frames calculated using the spherical wall method. We find that the Galilean invariance breaking effects stemming from the lattice artifacts partially cancel those caused by the nonlocal smearing parameter. Due to this cancellation, the Galilean invariance breaking effect is small, and the Galilean invariance can be restored by introducing Galilean invariance restoration operators.
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