论文标题
面包板 - 贝克 - 霍斯多夫公式的流量方法：精确的结果
The flow method for the Baker-Campbell-Hausdorff formula: exact results
论文作者
论文摘要
从几何数字整合的文献中利用技术，我们提出了一种新的通用方法来计算BCH公式的精确表达式。该方法在其最大的普遍性中包括将感兴趣的谎言代数嵌入矢量字段代数的子代数中，以某种方式通过同构形态性，因此，可以从原始代数的两个元素的BCH公式可以从相应矢量场的流量的组成的组成中恢复。因此，我们称我们的方法为流量方法。显然，在可以通过分析计算流量的情况下，此方法具有很大的优势。我们在某些可以直接应用的基准示例上说明了它的有用性，并讨论了无法获得精确表达的情况的一些可能的扩展。
Leveraging techniques from the literature on geometric numerical integration, we propose a new general method to compute exact expressions for the BCH formula. In its utmost generality, the method consists in embedding the Lie algebra of interest into a subalgebra of the algebra of vector fields on some manifold by means of an isomorphism, so that the BCH formula for two elements of the original algebra can be recovered from the composition of the flows of the corresponding vector fields. For this reason we call our method the flow method. Clearly, this method has great advantage in cases where the flows can be computed analytically. We illustrate its usefulness on some benchmark examples where it can be applied directly, and discuss some possible extensions for cases where an exact expression cannot be obtained.
