Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct structure-preserving algorithms, but without exquisite considerations, it can easily break the Lorentz invariance of continuous systems. In this paper, we introduce a Lorentz invariant splitting technique to construct high order explicit Lorentz invariant volume-preserving algorithms (LIVPAs) for simulating charged particle dynamics. Using this method, long-term stable explicit LIVPAs with different orders are developed and their performances of Lorentz invariance and long-term stability are analyzed in detail.

Lorentz不变结构保留算法具有与参考无关的长期稳定性，这对于模拟相对论多尺度动力学过程至关重要。分裂方法已被广泛地用于构造保留结构的算法，但是如果没有精妙的考虑，它很容易打破连续系统的洛伦兹不变性。在本文中，我们介绍了一种Lorentz不变分裂技术，以构建用于模拟带电粒子动力学的高阶显式Lorentz不变体积保留算法（LIVPA）。使用这种方法，开发了具有不同阶数的长期稳定的显式LIVPA，并详细分析了它们的洛伦兹不变性和长期稳定性。