标题： 变分法在孤子上的激发费米子研究 显示英文标题

标题： Variational Approach to Excited Fermions on Kinks

摘要： 我们研究了在1个空间和1个时间维度中费米子场对孤子解的反作用。 我们采用变分法来确定总能量最小值的上限。 该能量有三个贡献：经典孤子能量、价态费米子能量以及费米子真空极化能量。 后者源于孤子与狄拉克海的相互作用，并且对于费米子半经典展开的一致性是必需的。 早期的研究仅考虑了价态部分，并观察到了显著的反作用。 这体现在孤子轮廓的明显畸变上。 我们发现，当正确考虑狄拉克海时，这种畸变被大大缓解。 结果是，反作用仅导致孤子轮廓的轻微挤压或拉伸。 显示英文摘要

摘要： We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink energy, the energy of valence fermions and the fermion vacuum polarization energy. The latter arises from the interaction of the kink with the Dirac sea and is required for consistency of the semi-classical expansion for the fermions. Earlier studies only considered the valence part and observed a substantial back-reaction. This was reflected by a sizable distortion of the kink profile. We find that this distortion is strongly mitigated when the Dirac sea is properly accounted for. As a result the back-reaction merely produces a slight squeeze or stretch of the kink profile.