论文标题
关于非相关主义量子力学和电磁学
About non-relativistic quantum mechanics and electromagnetism
论文作者
论文摘要
我们在这里描述了在非相互作用的带电颗粒的非相互量子机械多体型理论中电磁学的连贯表述。我们在QED精神上使用了田间理论的数学框架及其量化。这是必要的，因为出现了误解的多种流形，尤其是在磁场和仪表不变性方面。情况是由量子力学的历史发展决定的，从给定的电磁场的存在下，从单个粒子的schrödinger方程开始，随后是许多具有库仑相互作用的许多带电相同粒子的多体理论。我们对非权利主义QED的方法强调了仪表不变性和外部场的作用。我们进一步开发了该理论的$ 1/c^2 $近似，允许对没有光子的相互作用带电粒子进行封闭描述。由此产生的汉密尔顿人与量化的Darwin Hamiltonian的量化版本相吻合，该版本还包含库仑以外的电流电流磁相互作用。我们在一些示例中展示了多体理论扩展的重要性。
We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because a manifold of misinterpretations emerged especially regarding the magnetic field and gauge invariance. The situation was determined by the historical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions. Our approach to the non-relativistic QED emphasizes the role of the gauge-invariance and of the external fields. We develop further the $1/c^2$ approximation of this theory allowing a closed description of the interacting charged particles without photons. The resulting Hamiltonian coincides with the quantized version of the Darwin Hamiltonian containing besides the Coulomb also a current-current diamagnetic interaction. We show on some examples the importance of this extension of the many-body theory.
