发表机构
Middlebury College; Stellenbosch University（明德学院; 斯坦伦布什大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究计算了2+1维非奇异宇宙弦背景下标量场的真空极化能，将其表示为散射数据的重整化求和与积分，通过局域与全局态密度关系实现微扰重整化条件的精确应用。
AI 中文摘要
我们计算了2+1维时空中非奇异宇宙弦背景下标量场的真空极化能（VPE）。我们的计算将VPE表示为散射数据的重整化求和与积分，对于类似曲率方势阱的“圆珠笔”模型，该散射数据可通过勒让德函数和贝塞尔函数表示；对于一般弦轮廓，则可通过数值方法获得。我们展示了以格林函数表示的局域态密度与以约斯特函数表示的全局态密度之间的关系如何扩展到该弯曲时空背景，从而实现微扰重整化条件的精确应用。
英文摘要
We calculate the vacuum polarization energy (VPE) of a scalar field in the background of a nonsingular cosmic string in $2+1$ spacetime dimensions. Our calculation expresses the VPE as a renormalized sum and integral over scattering data, which can be expressed in terms of Legendre and Bessel functions for the "ballpoint pen" model, analogous to a square well in curvature, and which can be obtained numerically for a generic string profile. We show how relationships between the local density of states, expressed in terms of the Green's function, and the global density of states, expressed in terms of the Jost function, extend to this curved spacetime background and allow for precise implementation of perturbative renormalization conditions.
Comments9 pages, 1 figure; v2: updated title, added clarifying comments, fixed typos, version to appear in PRD
Journal refPhys. Rev. D 114 (2026) 085004
