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arXiv · 2310.10680

On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$

Sadataka Furui
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Abstract

We study application of the Clifford algebra and the Grassmann algebra to image recognitions in $(3+1)D$ using quaternions. Following S.L.Adler, we construct a quaternion-valued wave function model with fermions and bosons of equal degrees of freedom, similar to Cartan's supersymmetric model. The Clifford algebra ${\mathcal A}_{3,1}$ is compared with ${\mathcal A}_{2,1}$ and the model applied to the $(2+1)D$ non-destructive testing is extended. The fixed point lattice actions are calculated for 7 paths in $(3+1)D$ space with lengths less than or equal to 8 lattice units. Comparison with the quaternion time approach of Ariel, quaternion Fourier transform of Hitzer and the tensor renormalization group approach to classical lattice models are also discussed.

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Sadataka Furui. 2023-10-12. On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$. https://arxiv.org/abs/2310.10680

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