Beyond the Wedge Product: A Novel Decomposition of the Geometric Product
2025-05-23
This paper introduces a new operation called the "transwedge product," which completely decomposes the geometric product into fundamental operations of exterior algebra: the exterior product, left and right complements, and application of the metric. The author demonstrates that the transwedge product generates a spectrum of products ranging from the exterior product to the interior product (contraction), replacing the commutator product and offering a cleaner way to compute the geometric product. This applies not only to three dimensions but also to higher-dimensional geometric algebras, with practical applications in conformal geometric algebra, such as calculating circles intersecting orthogonally.
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