论文标题
流动方程方法朝着分离能量分离的汉密尔顿统一，等效于与电磁场耦合的狄拉克·哈密顿
A Flow Equation Approach Striving Towards an Energy-Separating Hamiltonian Unitary Equivalent to the Dirac Hamiltonian with Coupling to Electromagnetic Fields
论文作者
论文摘要
Dirac Hamiltonian $ h^{\ left（d \ right）} $，用于相对论充电的费用最小化的耦合到（可能是时间依赖的）电磁场（可能是时间依赖的）电磁场通过专用构建的流动方程方法进行转换，因此该转换的结果与$ h^{\ weart weft（\ prive to progn contive and prime to t to $ h^） $ h^{\ left（nw \ right）} $与dirac $β$ -matrix通勤。扩展$ h^{\ left（nw \ right）} $，以$ \ frac {v^2} {c^2} $schrödinger-pauli Quantum Magintics的非余地hamiltonian $ h^{\ left（sp \ right）} $当前领先的订单时出现了schrödinger-pauli量子机械师的出现。以Magnus类型系列的扩展为幌子，明确考虑了对$ H^{\ left（sp \ firt）} $的所有相对论更正，该系列系数生成的系列系数$ \ left（\ frac {v^{v^{2}}}}}} {c^{2}} {c^{c^{2}} $ qe for仅迭代换向器。在静态场的特殊情况下，流动方程方法与众所周知的能量分离的埃里克森的单一转换的等效性是基于将$β$ -Matrix转化为与$ h^{\ h^{\ weft（d \ right）$相关的反向流动方程的精确解决方案。这样，身份$ h^{\ left（nw \ right）} =β\ sqrt {h^{h^{\ left（nw \ right）} h^{\ left（nw \ right）}} $是确定的，暗示$ h^{\ h^{\ weft（nw \ right）} $。
The Dirac Hamiltonian $H^{\left(D\right)}$ for relativistic charged fermions minimally coupled to (possibly time-dependent) electromagnetic fields is transformed with a purpose-built flow equation method, so that the result of that transformation is unitary equivalent to $H^{\left(D\right)}$ and granted to strive towards a limiting value $H^{\left(NW\right)}$ commuting with the Dirac $β$-matrix. Upon expansion of $H^{\left(NW\right)}$ to order $\frac{v^2}{c^2}$ the nonrelativistic Hamiltonian $H^{\left(SP\right)}$ of Schrödinger-Pauli quantum mechanics emerges as the leading order term adding to the rest energy $mc^2$. All the relativistic corrections to $H^{\left(SP\right)}$ are explicitly taken into account in the guise of a Magnus type series expansion, the series coefficients generated to order $\left(\frac{v^{2}}{c^{2}}\right)^{n}$ for $n\geq2$ comprising partial sums of iterated commutators only. In the special case of static fields the equivalence of the flow equation method with the well known energy-separating unitary transformation of Eriksen is established on the basis of an exact solution of a reverse flow equation transforming the $β$-matrix into the energy-sign operator associated with $H^{\left(D\right)}$. That way the identity $H^{\left(NW\right)}=β\sqrt{H^{\left(NW\right)}H^{\left(NW\right)}}$ is established implying $H^{\left(NW\right)}$ being determined unambiguously.
