On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916091041677312 |
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| author | Furui, Sadataka |
| author_facet | Furui, Sadataka |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_10680 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$ Furui, Sadataka Mathematical Physics High Energy Physics - Lattice High Energy Physics - Phenomenology 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. |
| title | On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$ |
| topic | Mathematical Physics High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2310.10680 |