破坏性相对论是一种破坏性的相对论
Maria Przybylska1, Wojciech Szumiński1, Andrzej J Maciejewski2
1Institute of Physics, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland.
Chaos (Woodbury, N.Y.)
|June 27, 2023
概括
我们为高能粒子的相对论汉密尔顿方程的可整合性推导出了新的,强有力的条件. 这些条件适用于弱场,简化了使用线性代数的分析,并且比非相对论对应条件更严格.
科学领域:
- 理论物理 理论物理
- 经典机械 经典机械 经典机械
- 特别相对论的特殊相对论.
背景情况:
- 描述高能粒子动态需要特殊相对论的框架.
- 分析相对论运动方程的属性对于理论物理学来说至关重要.
研究的目的:
- 制定和分析相对论汉密尔顿方程在弱外界界限中的必要整合性条件.
- 建立相对论和非相对论系统的整合性之间的关系.
主要方法:
- 在条件下对运动的汉密尔顿方程进行分析 2V(q) ≪mc2.2.
- 对于是坐标的同质函数的潜在的可整合性条件的制定.
- 调查 Liouville 整合性的缩放式赫森矩阵的固有值.
主要成果:
- 为相对论系统的整合性推导出强有力的,一般的必要条件.
- 表明这些条件比非相对论系统的条件要强得多.
- 证明计算简化为线性代数,使条件易于应用.
结论:
- 衍生条件为分析相对论哈密尔顿系统提供了强大的工具.
- 对于多项式同质潜能,只有依赖于单个坐标或半径形式的系统似乎可以在相对论领域中整合.
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