Calculation of Spin Group Elements Revisited
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913809500733440 |
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| author | Shirokov, D. S. |
| author_facet | Shirokov, D. S. |
| contents | In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in the case of arbitrary dimension and signature, and then explicitly using matrices, quaternions, and split-quaternions in the cases of all possible signatures (p,q) of space up to dimension n=p+q=3. The different formalisms are convenient for different possible applications in physics, engeneering, and computer science. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_02772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calculation of Spin Group Elements Revisited Shirokov, D. S. Mathematical Physics 15A66, 11E88 In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in the case of arbitrary dimension and signature, and then explicitly using matrices, quaternions, and split-quaternions in the cases of all possible signatures (p,q) of space up to dimension n=p+q=3. The different formalisms are convenient for different possible applications in physics, engeneering, and computer science. |
| title | Calculation of Spin Group Elements Revisited |
| topic | Mathematical Physics 15A66, 11E88 |
| url | https://arxiv.org/abs/2412.02772 |