论文标题
电磁系统的高级非层次化哈密顿
The high-order nonrelativistic Hamiltonian of electromagnetic system
论文作者
论文摘要
通过应用道格拉斯 - 凯罗尔·霍恩·霍恩（Douglas-Kroll-Hess）方法，研究了电磁场中标量，旋转器和载体颗粒的非同性汉密尔顿人。他们的相对主义哈密顿人在潜力上扩大了，并衍生出了包含一人和两光子潜力的汉密尔顿人。通过在动量上应用Taylor扩展，获得了高达$Mα^8 $订单的非同性汉密尔顿人，并且Spin-1/2旋转器的结果与在参考文献中应用散射匹配方法获得的结果相吻合。修订版A {\ bf 100}，012513（2019）]。然后，库仑系统的哈密顿量的奇异性被分开并取消。获得了Scaleer的正规化哈密顿量最高为$Mα^8 $订单，并且获得了库仑电场中的电子。相对论校正的数值结果与相对论理论相吻合。还得出了库仑场的多电子的正规化哈密顿量最高$Mα^6 $。
The nonrelativistic Hamiltonians of scalar, spinor and vector particles in the electromagnetic field are studied by applying the Douglas-Kroll-Hess approach. Their relativistic Hamiltonians are expanded on the potential, and the Hamiltonians containing one- and two-photon potentials are derived. The nonrelativistic Hamiltonians up to $mα^8$ order are obtained by applying Taylor expansion on momentum, and the result of spin-1/2 spinor is coincided with the result obtained by applying scattering matching approach in the Ref.~[Phys. Rev. A {\bf 100}, 012513 (2019)]. Then, the singularities in Hamiltonian of Coulomb systems are separated out and cancelled. The regularized Hamiltonian up to $mα^8$ order for scaler and electron in Coulomb field are obtained. The numerical results of relativistic corrections are coincided with the relativistic theory. The regularized Hamiltonian up to $mα^6$ for multi-electrons in Coulomb field are also derived.
