标题： 具有杂质的任意维数量场：一阶框架与精确解 显示英文标题

标题： Scalar fields with impurities in arbitrary dimensions: first-order framework and exact solutions

摘要： 我们研究了一类标量场模型与任意时空维度中杂质耦合的情况。 该系统允许引入一个二阶张量，如果满足一个与运动方程一致的一阶微分方程，则该张量可以被强制服从某种等式。 对于静态解的情况，系统的能量密度可以等于一个辅助矢量函数的散度，这个辅助函数被引入以帮助我们求解模型。 研究了在自变量缩放下场构型的稳定性，并通过考虑不同的典型模型来说明这一过程。 结果显示，在任意维度下都可以得到精确解，这与一阶方程的存在密切相关。 显示英文摘要

摘要： We study a class of scalar field models coupled to impurities in arbitrary spacetime dimensions. The system admits the introduction of a second-order tensor that can be forced to obey an equality, if a first-order differential equation is satisfied, compatible with the equation of motion when the potential engenders a very specific form. In the case of static solutions, the energy density of the system can equal the divergence of an auxiliary vector function, which is included to help us solve the model. Stability of the field configuration under rescale of argument is investigated, and the procedure is illustrated considering distinct canonical models. The results show that exact solutions can be obtained in arbitrary dimensions, related to the presence of the first-order equation.