横向物质哈密顿量
The transverse matter Hamiltonian
- Istituto di Struttura della Materia and Division of Ultrafast Processes in Materials (FLASHit) of the National Research Council（国家研究委员会材料结构研究所和超快过程材料分部(FLASHit)）
- Department of Physics and Materials Science, University of Luxembourg（卢森堡大学物理与材料科学系）
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AI总结：
本研究将费米的经典高斯方程推导方法推广到矢量势的横向分量，通过量子正则变换得到符合规范不变性的物质哈密顿量，避免微扰理论失效，还揭示了声子等基本激发电磁劈裂的量子起源。
AI中文摘要：
恩里科·费米在1932年利用经典高斯方程从纵向电磁势推导出库仑密度-密度相互作用。本研究将费米的方法推广到矢量势的横向分量，通过完全量子化的正则变换，将横向矢量势替换为电流-电流及电流-电流-密度相互作用。随后将变换后的哈密顿量投影到费米子空间，得到仅含物质、完全非相干且符合规范不变性的哈密顿量。这种相干性的消除可避免哈格定理所预测的微扰理论失效，还能在变换后的空间中引入图论方法。在讨论横向相互作用对基于费米方法的现有理论的影响后，研究结论表明，该横向哈密顿量为声子及其他基本激发的电磁纵向-横向劈裂提供了量子起源。
英文摘要：
Enrico Fermi in 1932 used classical Gauss equation to derive the Coulomb density--density interaction from the longitudinal electromagnetic potential. In this work we extend the Fermi procedure to the transverse component of the vector potential. By using a fully quantum canonical transformation, we replace the transverse vector potential with a current--current and current--current--density interactions. The transformed Hamiltonian is, then, projected in the fermionic space providing a matter--only, totally incoherent and gauge respecting Hamiltonian. The removal of coherence will avoid the breakdown of perturbation theory predicted by Haag's theorem, and make possible to introduce, in the transformed space, the diagrammatic approach. After discussing the implications of the transverse interactions on the current theories based on the Fermi procedure, we conclude by showing how the transverse Hamiltonian provides the quantum origin of the electromagnetic longitudinal--transverse splitting of phonons and other elemental excitations.
