The Poincare lemma for codifferential, anticoexact forms, and applications to physics
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arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866908375389831168 |
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| author | Kycia, Radosław Antoni |
| author_facet | Kycia, Radosław Antoni |
| contents | The linear homotopy theory for codifferential operator on Riemannian manifolds is developed in analogy to a similar idea for exterior derivative. The main object is the cohomotopy operator, which singles out a module of anticoexact forms from the module of differential forms defined on a star-shaped open subset of a manifold. It is shown that there is a direct sum decomposition of a differential form into coexact and anticoexat parts. This decomposition gives a new way of solving exterior differential systems. The method is applied to equations of fundamental physics, including vacuum Dirac-Kähler equation, coupled Maxwell-Kalb-Ramond system of equations occurring in a bosonic string theory and its reduction to the Dirac equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_08542 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Poincare lemma for codifferential, anticoexact forms, and applications to physics Kycia, Radosław Antoni Differential Geometry Mathematical Physics The linear homotopy theory for codifferential operator on Riemannian manifolds is developed in analogy to a similar idea for exterior derivative. The main object is the cohomotopy operator, which singles out a module of anticoexact forms from the module of differential forms defined on a star-shaped open subset of a manifold. It is shown that there is a direct sum decomposition of a differential form into coexact and anticoexat parts. This decomposition gives a new way of solving exterior differential systems. The method is applied to equations of fundamental physics, including vacuum Dirac-Kähler equation, coupled Maxwell-Kalb-Ramond system of equations occurring in a bosonic string theory and its reduction to the Dirac equation. |
| title | The Poincare lemma for codifferential, anticoexact forms, and applications to physics |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2009.08542 |