标题： 普罗卡孤子的真空极化能 显示英文标题

标题： Vacuum Polarization Energy of a Proca Soliton

摘要： 我们研究了一个扩展的Proca模型，在一维空间和一维时间维度中包含一个标量场和一个质量矢量场。 我们构造了孤子解，并随后计算了真空极化能（VPE），这是对孤子经典能量的主要量子修正。 为了进行此计算，我们采用了谱方法，这种方法高度依赖于Jost函数的解析性质。 该函数是从量子涨落与由孤子产生的背景势的相互作用中提取出来的。 特别是我们探讨了可能由质量间隙和矢量场涨落纵向分量的非常规归一化所引起的非解析成分。 通过数值模拟，我们验证了这些障碍实际上并不存在，并且VPE的真实动量和虚动量表述给出了相同的结果。 Jost函数的Born近似在实施标准重整化条件时至关重要。 在此背景下，我们解决了由于与质量间隙中能量相关的实动量对应的Born近似为虚数而出现的问题。 显示英文摘要

摘要： We study an extended Proca model with one scalar field and one massive vector field in one space and one time dimensions. We construct the soliton solution and subsequently compute the vacuum polarization energy (VPE) which is the leading quantum correction to the classical energy of the soliton. For this calculation we adopt the spectral methods approach which heavily relies on the analytic properties of the Jost function. This function is extracted from the interaction of the quantum fluctuations with a background potential generated by the soliton. Particularly we explore eventual non-analytical components that may be induced by mass gaps and the unconventional normalization for the longitudinal component of the vector field fluctuations. By numerical simulation we verify that these obstacles do actually not arise and that the real and imaginary momentum formulations of the VPE yield equal results. The Born approximation to the Jost function is crucial when implementing standard renormalization conditions. In this context we solve problems arising from the Born approximation being imaginary for real momenta associated with energies in the mass gap.