标题： Proca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中包含一个纯量场和一个有质量的矢量场。我们构造了孤子解，并随后计算了真空极化能（VPE），这是孤子经典能量的主要量子修正项。为了进行此计算，我们采用了基于Jost函数解析性质的谱方法。这个函数是从量子涨落与由孤子生成的背景势之间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以及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的真实动量和虚部动量形式给出了相同的结果。当实施标准重整化条件时，Jost函数的Born近似至关重要。在此背景下，我们解决了由于Born近似对于与质量间隙相关的实动量为虚数而产生的问题。 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.