Infrared finite scattering theory in quantum field theory and quantum gravity
Infrared finite scattering theory in quantum field theory and quantum gravity
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DOI：
10.1103/physrevd.106.066005
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发表时间：
2022-03
影响因子：
5
通讯作者：
Kartik Prabhu;Gautam Satishchandran;R. Wald
中科院分区：
文献类型：
--
作者：
Kartik Prabhu;Gautam Satishchandran;R. Wald
最早的量子场理论（QFT），红外发散出现在无质量场的散射理论中。这些红外发散是记忆效应的表现：在1 /r阶，无质量场一般不会在延迟时间后期（u → + ∞）恢复到与延迟时间早期（u → −∞）相同的值。具有记忆的状态并不奇异，但它们并不位于标准的Fock空间中。红外发散仅仅是试图在标准Fock空间中用记忆表示状态的人为产物。- 矩阵，以及希尔伯特电动力学带电场。带电粒子的配对本征态记忆了空间无限域上消失的大规范电荷的电磁场表示，以及空间无限域上共线超平移电荷的带电过程。同样，Faddeev-Kulish“修整”过程不会产生所需的本征态，因为修整有助于零记忆体的吸收。我们证明了在远离真空的空间无限远处，不存在超平移电荷的本征态。因此，类似的Faddeev-Kulish结构在量子引力中会灾难性地失败。我们研究了Faddeev-Kulish结构的一些替代方案，但发现这些也不起作用。我们相信，如果人们希望在量子引力的基本水平上处理散射--以及在无质量QED和杨-米尔斯理论中--就有必要从代数的观点来处理“进”和“出”态，其中人们不试图将这些态“硬塞进”预先选择的“进”和“出”希尔伯特空间。我们概述了这样一个散射理论的框架，这将是明显的红外有限。
earliest of quantum field theory (QFT) that infrared divergences arise in scattering theory with massless fields. These infrared divergences are manifestations of the memory effect: At order 1 /r a massless field generically will not return to the same value at late retarded times ( u → + ∞ ) as it had at early retarded times ( u → −∞ ). There is nothing singular about states with memory, but they do not lie in the standard Fock space. Infrared divergences are merely artifacts of trying to represent states with memory in the standard Fock space. -matrix, and Hilbert electrodynamics charged field. pairing eigenstates of the charged particles memory representations of the electromagnetic field of vanishing large gauge charges at spatial the charged procedure for with of collinear supertranslation charges at spatial infinity. Again, the Faddeev-Kulish “dressing” procedure does not produce the desired eigenstates because the dressing contributes to the null memory flux. We prove that there are no eigenstates of supertranslation charges at spatial infinity apart from the vacuum. Thus, analogs of the Faddeev-Kulish construction fail catastrophically in quantum gravity. We investigate some alternatives to Faddeev-Kulish constructions but find that these also do not work. We believe that if one wishes to treat scattering at a fundamental level in quantum gravity — as well as in massless QED and Yang-Mills theory — it is necessary to approach it from an algebraic viewpoint on the “in” and “out” states, wherein one does not attempt to “shoehorn” these states into some pre-chosen “in” and “out” Hilbert spaces. We outline the framework of such a scattering theory, which would be manifestly infrared finite.