Jackiw-Rebbi模型。玻色/费米单圈扭结质量移动
The Jackiw-Rebbi model. Bose/Fermi one-loop Kink mass shifts
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中文总结 AI 辅助
本文在Jackiw-Rebbi模型中计算玻色/费米单圈扭结质量移动，推广DHN方案至费米子，并发展费曼式量子化，确保Berezin积分与DHN结果一致。
中文摘要 AI 辅助
在Jackiw-Rebbi模型中总结了标量和旋量扭结涨落。正则量子化通常通过将标量和旋量场展开系数提升为玻色/费米产生和湮灭算符来实现。玻色子的单粒子态由薛定谔方程的标量本征函数提供，费米子的单粒子态由狄拉克哈密顿量的本征旋量提供，这些本征函数在基态或扭结背景上求值。计算了由玻色子或费米子诱导的单圈扭结质量移动。当量子被扭结俘获或散射时，束缚态和散射态都有贡献。扭结涨落的玻色和费米零模在单圈阶不改变扭结质量。在正则量子化框架中推导的Dashed-Hasslacher-Neveu（DHN）方案被推广到费米子领域。另外，发展了在扭结标量和旋量涨落空间中Jackiw-Rebbi模型的费曼式量子化。确保对扭结旋量涨落的Grassmann系数进行Berezin积分，得到与在DHN范式中包含费米统计所揭示的相同情景，至少在扭结Casimir能量的计算方面如此。
英文摘要
Scalar and spinor Kink fluctuations are summarized in the Jackiw-Rebbi model. Canonical quantization is conventionally achieved by promoting the coefficients of the scalar and spinor field expansions to bosonic/fermionic creation/annihilation operators. One-particle states for bosons, respectively for fermions, are supplied by the scalar eigenfunctions of the Schr$\ddot{\rm o}$dinger, respectively, the eigenspinors of the Dirac Hamiltonian, evaluated either on the ground state or the Kink background. One-loop kink mass shifts are computed induced either by bosons or fermions. Both bound and scattering states contribute when the quanta are trapped by or scattered off the Kink. Zero modes of Kink fluctuations bosonic and fermionic do not modify the Kink mass at one-loop order. The Dashed-Hasslacher-Neveu prescription, derived in the canonical quantization framework, is generalized to the fermionic realm. Alternatively, quantization à la Feynman of the Jackiw-Rebbi model in the spaces of Kink scalar and spinor fluctuations is developed. It is ensured that Berezin integration over the Grassmann coefficients of the Kink spinor fluctuations leads to identical scenario as that revealed by including Fermi statistics in the DHN paradigm, at least with respect to the computation of the Kink Casimir energy.
发表机构
- Universidad de Salamanca（萨拉曼卡大学）
机构由 AI 辅助整理，请以论文原文为准。
