红外问题与规范选择：经典Dirac场的散射
Infrared problem vs gauge choice: scattering of classical Dirac field
摘要：
我们考虑狄拉克方程的经典旋量场放置在一个外部的，时间相关的电磁场的形式典型的散射设置：$F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$，其中电流产生$F^{\mathrm{ret}/\mathrm{adv}}$有过去和未来的渐近线均匀度$-3$，和自由场$F^{\mathrm{in}/\mathrm{out}}$的电流产生的辐射场具有类似的渐近行为。我们证明了电磁规范的存在，其中粒子有“在”和“出”渐近状态接近自由场状态，没有长时间的自由动力学修正。使用一个特殊的柯西叶的时空，我们表明在这种情况下的存在性和渐近完备性的波算子。此外，我们定义了一个特殊的“演化图”，其中自由演化算子对$t\to\pm\infty$有明确的限制，因此散射波算子不需要自由演化抵消。
英文摘要：
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.
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