We consider topological defects for the $\lambda {\varphi }^4$ theory in (1+1) dimensions with a Lorentz-violating background. It has been shown, by M. Barreto et al. (2006) [34], one cannot have original effects in (the leading order of) single scalar field model. Here, we introduce a new Lorentz-violating term, next to leading order which cannot be absorbed by any redefinition of the scalar field or coordinates. Our term is the lowest order term which leads to concrete effects on the kink properties. We calculate the corrections to the kink shape and the corresponding mass. Quantization of the kink is performed and the revised modes are obtained. We find the bound and continuum states are affected due to this Lorentz symmetry violation.

我们考虑了拓扑缺陷 $\lambda {\varphi }^4$（1 + 1）维的理论，违反了洛伦兹的背景。M. Barreto等人已经证明了这一点。（2006）[34]，在单标量场模型（的领先顺序）中不可能有原始效果。在这里，我们在领先顺序旁边引入了一个新的违反Lorentz的术语，它不能被标量场或坐标的任何重新定义所吸收。我们的术语是最低阶的术语，可导致对纽结特性的具体影响。我们计算扭结形状和相应质量的校正量。进行纽结的量化并获得修正的模式。我们发现由于这种洛伦兹对称性违背，边界状态和连续状态受到影响。