非均匀磁场中的QCD真空
QCD Vacuum in an Inhomogeneous Magnetic Field
AI总结：
本文在手征微扰论框架下，研究非均匀磁场对QCD真空的影响，计算相关零温物理量并推导诱导真空电流，通过与局域常数近似对比探测真空的空间响应与非局域结构。
AI中文摘要：
本文在手征微扰论框架下研究非均匀磁场对QCD真空的影响。所选磁场沿某一空间方向局域分布，其对应的量子力学问题可精确求解。研究特别关注采用维数正规化进行正则化与重整化的过程。磁场的非零梯度要求在手征微扰论中引入额外算符，这些算符的效应出现在手征展开的次领头阶。因此，平衡真空可观测量的磁场依赖关系可在次领头阶确定，且无待定参数。我们计算了零温下非均匀背景中的自由能与手征凝聚，包括积分量和空间分辨的局域可观测量。与局域常数近似的对比可直接探测磁化QCD真空的空间响应与非局域结构。此外，我们还推导了与磁场非均匀性相关的诱导真空电流。
英文摘要：
The effect of an inhomogeneous magnetic field on the QCD vacuum is addressed using the framework of chiral perturbation theory. The magnetic field is chosen to be localized along one spatial direction, with a profile for which the underlying quantum mechanical problem is exactly solvable. Particular attention is paid to regularization and renormalization using dimensional regularization. While the non-vanishing gradient of the magnetic field requires additional operators in chiral perturbation theory, their effect occurs at next-to-next-to-leading order in the chiral expansion. Consequently, the magnetic field dependence of equilibrium vacuum observables can be determined at next-to-leading order without undetermined parameters. We compute the zero-temperature free energy and chiral condensate for the inhomogeneous background, both as integrated quantities as well as spatially resolved local observables. Comparison with locally constant approximations enables a direct probe of the spatial response and nonlocal structure of the magnetized QCD vacuum. We additionally derive the induced vacuum current associated with the inhomogeneity of the magnetic field.
