量子扭结质量的显式有限导子
Manifestly Finite Derivation of the Quantum Kink Mass
摘要：
1974年，达申、哈斯拉赫和奈芙计算了1+1维标量$ϕ^4$理论中扭结质量的量子修正。推导依赖于识别的扰动扭结的解决方案的Poschl-Teller（PT）理论。他们把理论放在一个周期性的盒子里，使之正规化，尽管扭结本身并不是周期性的。他们还需要一个特设的平面波和PT状态的识别，这是很难解释的解压缩限制。我们重新推导的质量使用扭结算子重铸这个问题的PT哈密顿量，我们明确对角化使用其确切的本征态。我们从一开始就正规化，使我们的理论是有限的，因此不需要紧化。在我们的扭结质量的最终表达式中，PT势的形式消失了，这表明我们的质量公式适用于其他量子孤子。
英文摘要：
In 1974 Dashen, Hasslacher and Neveu calculated the leading quantum correction to the mass of the kink in the scalar $ϕ^4$ theory in 1+1 dimensions. The derivation relies on the identification of the perturbations about the kink as solutions of the Poschl-Teller (PT) theory. They regularize the theory by placing it in a periodic box, although the kink is not itself periodic. They also require an ad hoc identification of plane wave and PT states which is difficult to interpret in the decompactified limit. We rederive the mass using the kink operator to recast this problem in terms of the PT Hamiltonian which we explicitly diagonalize using its exact eigenstates. We normal order from the beginning, rendering our theory finite so that no compactification is necessary. In our final expression for the kink mass, the form of the PT potential disappears, suggesting that our mass formula applies to other quantum solitons.
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