走向相对论性原子物理学。II。带电粒子加电磁场系统的集体相对论变量
Towards Relativistic Atomic Physics. II. Collective and Relative Relativistic Variables for a System of Charged Particles plus the Electro-Magnetic Field
摘要：
在这第二篇论文中，我们完成了一个孤立系的经典描述的“带电正能量粒子，与格拉斯曼值的电荷和相互库仑相互作用，加上一个横向的电磁场“在静止框架即时形式的动力学。特别是，我们将展示如何确定一个集体变量与内部3-中心的质量上的瞬时3-空间，消除与约束${\vec {\cal K}}_{(int)} \approx 0$。这里${\vec {\cal K}}_{(int)}$是庞加莱群的不忠实内部实现中的洛伦兹助推生成元，它的消失是固定到静止标架条件${\vec {\cal P}}_{(int)} \approx 0$的规范。我们展示了如何找到这个集体变量为以下孤立系：a）带电粒子与库仑加达尔文相互作用; b）横向辐射场; c）带电粒子与相互库仑相互作用加上横向电-磁场。然后我们定义了开粒子子系统的Dixon多极展开式。我们还定义了静止坐标系瞬时形式的原子物理学的相对论电偶极近似，并找到了电偶极表象的一个可能的相对论推广。
英文摘要：
In this second paper we complete the classical description of an isolated system of "charged positive-energy particles, with Grassmann-valued electric charges and mutual Coulomb interaction, plus a transverse electro-magnetic field" in the rest-frame instant form of dynamics. In particular we show how to determine a collective variable associated with the internal 3-center of mass on the instantaneous 3-spaces, to be eliminated with the constraints ${\vec {\cal K}}_{(int)} \approx 0$. Here ${\vec {\cal K}}_{(int)}$ is the Lorentz boost generator in the unfaithful internal realization of the Poincare' group and its vanishing is the gauge fixing to the rest-frame conditions ${\vec {\cal P}}_{(int)} \approx 0$. We show how to find this collective variable for the following isolated systems: a) charged particles with a Coulomb plus Darwin mutual interaction; b) transverse radiation field; c) charged particles with a mutual Coulomb interaction plus a transverse electro-magnetic field. Then we define the Dixon multipolar expansion for the open particle subsystem. We also define the relativistic electric dipole approximation of atomic physics in the rest-frame instant form and we find the a possible relativistic generalization of the electric dipole representation.
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