Université de Montpellier, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France.
Sci Rep. 2017 Sep 11;7(1):11115. doi: 10.1038/s41598-017-11076-5.
This article deals with the fundamental problem of light-matter interaction in the quantum theory. Although it is described through the vector potential in quantum electrodynamics, it is believed by some that a hamiltonian involving only the electric and the magnetic fields is preferable. In the literature this hamiltonian is known as the Power-Zienau-Woolley hamiltonian. We question its validity and show that it is not equivalent to the minimal-coupling hamiltonian. In this article, we show that these two hamiltonians are not connected through a gauge transformation. We find that the gauge is not fixed in the Power-Zienau-Woolley hamiltonian. The interaction term is written in one gauge whereas the rest of the hamiltonian is written in another gauge. The Power-Zienau-Woolley hamiltonian and the minimal-coupling one are related through a unitary transformation that does not fulfill the gauge fixing constraints. Consequently, they predict different physical results. In this letter, we provide the correct quantum theory in the multipolar gauge with a hamiltonian involving only the physical fields.
本文讨论了量子理论中光与物质相互作用的基本问题。尽管它是通过量子电动力学中的矢量势来描述的，但有些人认为，只包含电场和磁场的哈密顿量更为可取。在文献中，这个哈密顿量被称为 Power-Zienau-Woolley 哈密顿量。我们质疑其有效性，并表明它与最小耦合哈密顿量不等价。在本文中，我们证明这两个哈密顿量之间没有通过规范变换连接。我们发现 Power-Zienau-Woolley 哈密顿量中的规范未被固定。相互作用项是在一个规范中写出的，而哈密顿量的其余部分是在另一个规范中写出的。Power-Zienau-Woolley 哈密顿量和最小耦合哈密顿量通过不满足规范固定约束的幺正变换相关。因此，它们预测了不同的物理结果。在这封信中，我们在多极规范中提供了仅包含物理场的正确量子理论和哈密顿量。
