A Lorentzian SU(3)-covariant noncommutative KP hierarchy and hypercomplex gauge fields
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911395729113088 |
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| author | Magnot, Jean-Pierre |
| author_facet | Magnot, Jean-Pierre |
| contents | We propose a formal framework for a noncommutative Kadomtsev--Petviashvili (KP) hierarchy which is covariant under the action of $SU(3)$ and compatible with a Lorentzian structure encoded in a twisted quaternionic (or Clifford) algebra. The starting point is a formal pseudodifferential operator $L$ built from an abstract derivation $D$ of Dirac type and coefficients in an associative algebra $\A$ that combines spin degrees of freedom (twisted quaternions, Clifford algebras) and color degrees of freedom (an internal $SU(3)$ factor, possibly realized via the octonions). In this way we obtain a hierarchy of formal partial differential equations which are Lorentz invariant and $SU(3)$ covariant and can be interpreted as integrable sectors of nonabelian gauge theories in $(3+1)$ dimensions and of their dimensional reductions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17105 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Lorentzian SU(3)-covariant noncommutative KP hierarchy and hypercomplex gauge fields Magnot, Jean-Pierre Mathematical Physics Exactly Solvable and Integrable Systems We propose a formal framework for a noncommutative Kadomtsev--Petviashvili (KP) hierarchy which is covariant under the action of $SU(3)$ and compatible with a Lorentzian structure encoded in a twisted quaternionic (or Clifford) algebra. The starting point is a formal pseudodifferential operator $L$ built from an abstract derivation $D$ of Dirac type and coefficients in an associative algebra $\A$ that combines spin degrees of freedom (twisted quaternions, Clifford algebras) and color degrees of freedom (an internal $SU(3)$ factor, possibly realized via the octonions). In this way we obtain a hierarchy of formal partial differential equations which are Lorentz invariant and $SU(3)$ covariant and can be interpreted as integrable sectors of nonabelian gauge theories in $(3+1)$ dimensions and of their dimensional reductions. |
| title | A Lorentzian SU(3)-covariant noncommutative KP hierarchy and hypercomplex gauge fields |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2601.17105 |