Ultrarelativistic decoupling transformation for generalized Dirac equations
Ultrarelativistic decoupling transformation for generalized Dirac equations
复制标题
广义狄拉克方程的超相对论解耦变换
DOI：
10.1103/physreva.92.012101
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发表时间：
2015
影响因子：
2.9
通讯作者：
U. Jentschura
中科院分区：
文献类型：
--
作者：
J. H. Noble;U. Jentschura
Foldy-Woutheysen变换揭示了广义狄拉克哈密顿量的非相对论极限，对Schr‘o dinger-Pauli理论中的有效算符给予了直观的物理解释。我们在这里讨论相反的极端相对论极限，它需要使用根本不同的展开，其中狄拉克方程中的主要动力学项被粒子的质量和其他相互作用(势)项摄动，而不是相反。超相对论去耦合变换被应用于自由狄拉克粒子(在Weyl基中)和高能快子，它们是用完全洛伦兹协变方程描述的超光速粒子。发现了有效的引力相互作用。对于快子，高能极限中的主要引力相互作用项被证明是吸引的，并且等于高能极限中的亚光速狄拉克粒子(迟滞子)的主导项。
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\"{o}dinger--Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive, and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.