The Poincare lemma for codifferential, anticoexact forms, and applications to physics
Authors:
- Radosław Antoni Kycia
Abstract
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.
- Record ID
- CUTe1647a2f052a4787b7da3867a43242bd
- Publication categories
- ;
- Author
- Journal series
- Results in Mathematics, ISSN 1422-6383, e-ISSN 1420-9012, Quarterly
- Issue year
- 2022
- Vol
- 77
- No
- 5
- Pages
- [1-20]
- Article number
- 182
- Other elements of collation
- rys.; Bibliografia (na s.) - 18-20; Bibliografia (liczba pozycji) - 32; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 77, Iss. 5
- Keywords in English
- Poincare lemma, codifferential, anticoexact form, applications to physics, homotopy operator
- ASJC Classification
- ;
- DOI
- DOI:10.1007/s00025-022-01646-z Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s00025-022-01646-z Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 100
- Score source
- journalList
- Score
- Publication indicators
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTe1647a2f052a4787b7da3867a43242bd/
- URN
urn:pkr-prod:CUTe1647a2f052a4787b7da3867a43242bd
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.