论文标题
红外问题与量规选择：经典狄拉克场的散射
Infrared problem vs gauge choice: scattering of classical Dirac field
论文作者
论文摘要
我们考虑将经典纺纱场的DIRAC方程式放置在典型的散射设置的外部，时间依赖的电磁场中：$ f = f = f = f^\ mathrm {ret}+f^\ f^\ mathrm {in} $ f^{\ MATHRM {RET}/\ MATHRM {adv}} $具有均值$ -3 $的过去和未来均等，而免费字段$ f^{\ mathrm {in}/\ mathrm {out}} $是由类似的Asmptotor行为产生的辐射场。我们显示了粒子在接近自由野外状态的粒子中具有“和“ out”渐近状态的电磁测量值的存在，没有长期校正自由动力学。在这种情况下，使用时空的特殊牛uch叶叶，波算子的存在和渐近完整性。此外，我们定义了一个特殊的“进化图片”，其中自由进化运算符具有$ t \ to \ pm \ pm \ infty $的定义明确的限制，因此散射波运算符不需要免费的进化反作用。
We consider the Dirac equation for the classical spinor field placed in an external, time-dependent electromagnetic field of the form typical for scattering settings: $F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$, where the current producing $F^{\mathrm{ret}/\mathrm{adv}}$ has past and future asymptotes homogeneous of degree $-3$, and the free fields $F^{\mathrm{in}/\mathrm{out}}$ are radiation fields produced by currents with similar asymptotic behavior. We show the existence of the electromagnetic gauges in which the particle has 'in' and 'out' asymptotic states approaching free field states, with no long-time corrections of the free dynamics. Using a special Cauchy foliation of the spacetime we show in this context the existence and asymptotic completeness of the wave operators. Moreover, we define a special 'evolution picture' in which the free evolution operator has well-defined limits for $t\to\pm\infty$, thus the scattering wave operators do not need the free evolution counteraction.
