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arXiv 1509.00501physics.hist-ph
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向量代数战争:历史的观点

The vector algebra war: a historical perspective

James M. Chappell, Azhar Iqbal, John G. Hartnett, Derek Abbott

摘要:

目前在工程和物理学中有各种各样不同的矢量形式。例如,吉布斯的三向量,闵可夫斯基的四向量,量子力学中的复旋量,用于描述刚体旋转的四元数和Clifford几何代数中定义的向量。有了这样一系列的向量形式主义的使用,因此似乎还没有一个适合于整个科学的向量形式主义的普遍协议。这是令人惊讶的,因为十九世纪科学的主要目标之一是在三维空间中适当地描述向量。这种情况也有一个不幸的后果,那就是将知识分散在许多学科中,并且需要大量的时间和精力来学习各种形式主义。因此,我们历史上回顾了我们的各种矢量系统的发展,并得出结论,克利福德的多矢量最好地实现了目标,描述矢量量在三维空间,并提供了一个统一的矢量系统的科学。

英文摘要:

There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one of the primary goals of nineteenth century science was to suitably describe vectors in three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Clifford's multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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