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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Collective Lorentz invariant dynamics on a single 'polynomial' worldline
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Collective Lorentz invariant dynamics on a single 'polynomial' worldline

机译：单个“多项式”世界线上的集体洛伦兹不变动力学

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摘要

Consider a worldline of a pointlike particle parameterized by polynomial functions, together with the light cone ('retardation') equation of an inertially moving observer. Then a set of apparent copies, R-or C-particles, defined by the (real or complex conjugate) roots of the retardation equation will be detected by the observer. We prove that for any 'polynomial' worldline the induced collective dynamics of R-C particles obeys a whole set of canonical conservation laws (for total momentum, angular momentum and the analogue of mechanical energy). Explicit formulas for the values of total angular momentum and the analogue of total rest energy (rest mass) are obtained; the latter is 'self-quantized', i.e. for any worldline takes only integer values. The dynamics is Lorentz invariant though different from the canonical relativistic mechanics. Asymptotically, at large values of the observer's proper time, the R-C particles couple and then assemble into compact incoming/outgoing clusters. As a whole, the evolution resembles the process of (either elastic or inelastic) scattering of a beam of composite particles. Throughout the paper the consideration is purely algebraic, with no resort to differential equations of motion, field equations, etc.
机译：考虑由多项式函数参数化的点状粒子的世界线，以及惯性运动的观察者的光锥（“延迟”）方程。然后，观察者将检测到由延迟方程的（实数或复数共轭）根定义的一组表观拷贝R或C粒子。我们证明，对于任何“多项式”世界线，R-C粒子的诱导集体动力学都遵循一整套规范守恒定律（对于总动量，角动量和机械能的类似物）。得到了总角动量值和总静止能量（静止质量）类似物的显式公式;后者是“自我量化的”，即，对于任何世界线而言，仅采用整数值。动力学是洛伦兹不变的，尽管不同于经典的相对论力学。渐近地，在观察者的适当时间的较大值下，R-C粒子耦合，然后组装成紧凑的传入/传出簇。总体而言，演化过程类似于复合粒子束的（弹性或非弹性）散射过程。整篇文章中的考虑都是纯代数的，没有求助于运动的微分方程，场方程等。

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