再论因果微扰展开：重标度相互作用的狄拉克海
The Causal Perturbation Expansion Revisited: Rescaling the Interacting Dirac Sea
摘要：
因果微扰展开定义了存在依赖于时间的外场时的狄拉克海。它产生一个算子，其图像推广的真空解决方案的负能量，从而给出了一个规范分裂的解决方案空间成两个子空间。在给出了一个自包含的介绍的想法和技术，我们表明，该运营商一般不是幂等的。我们修改了标准的建设由一个重新标度的程序，给出了一个投影机上的广义负能量子空间。由此产生的重新标度的因果微扰膨胀唯一定义的费米子投影仪在狄拉克方程的一系列分布的解决方案。本文的技术核心是详细地计算了这种展开式的组合数学。本文还证明了通过幺正变换可以从自由投影子得到有相互作用的费米子投影子。最后，我们分析了光锥膨胀的重标度过程的后果。
英文摘要：
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is in general not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.
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