Phase Space structure on Clifford Algebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912826363215872 |
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| author | Robson, C. |
| author_facet | Robson, C. |
| contents | I argue that the Hodge structure on a Euclidean Clifford algebra $Cl(n)$ provides a way to generalise Kähler structure to higher dimensions, in the sense that the paired variables are now associated with $k-$ and $(n-k)-$ dimensional subspaces rather than with vectors. This puts a phase space structure on Clifford algebras, and so allows us to construct a Hamiltonian dynamics on these multilinear variables. This construction shows that alternating pairs of subspaces obey commuting and anticommuting dynamics, hinting that this construction is indeed a natural one, with interesting new behaviour. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_10381 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase Space structure on Clifford Algebras Robson, C. Mathematical Physics I argue that the Hodge structure on a Euclidean Clifford algebra $Cl(n)$ provides a way to generalise Kähler structure to higher dimensions, in the sense that the paired variables are now associated with $k-$ and $(n-k)-$ dimensional subspaces rather than with vectors. This puts a phase space structure on Clifford algebras, and so allows us to construct a Hamiltonian dynamics on these multilinear variables. This construction shows that alternating pairs of subspaces obey commuting and anticommuting dynamics, hinting that this construction is indeed a natural one, with interesting new behaviour. |
| title | Phase Space structure on Clifford Algebras |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.10381 |