广义Dirac方程的超相对论解耦变换
Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
摘要：
众所周知，Foldy-Wouthuysen变换可以揭示广义狄拉克汉密尔顿量的非相对论极限，为薛定谔-泡利理论中的有效算子提供直观的物理解释。我们在这里讨论相反的，超相对论的限制，这需要使用一个根本不同的扩展，在狄拉克方程中的领先的动力学项是由粒子的质量和其他相互作用（潜在的）条款，而不是反之亦然扰动。超相对论解耦变换适用于自由狄拉克粒子（外尔基）和高能量快子，这是一个完全洛伦兹协变方程描述的超光速粒子。对于快子，在高能极限下的主导引力相互作用项是吸引的，并且在高能极限下的主导引力相互作用项等于亚光速狄拉克粒子（慢子）的主导引力相互作用项。
英文摘要：
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 Schrödinger--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.
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