The poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator
Authors:
- Radosław Antoni Kycia
Abstract
The paper focuses on various properties and applications of thehomotopy operator, which occurs in the Poincar ́e lemma. In the first part,an abstract operator calculus is constructed, where the exterior derivativeis an abstract derivative and the homotopy operator plays the role ofan abstract integral. This operator calculus can be used to formulateabstract differential equations. An example of the eigenvalue problemthat resembles the fermionic quantum harmonic oscillator is presented.The second part presents the dual complex to the Dolbeault bicomplexgenerated by the homotopy operator on complex manifolds.
- Record ID
- CUT776c76ed6faf47628ca52e34fbf998c0
- Publication categories
- ;
- Author
- Journal series
- Results in Mathematics, ISSN 1422-6383, e-ISSN 1420-9012, Quarterly
- Issue year
- 2020
- Vol
- 75
- Pages
- [1-14]
- Article number
- 122
- Other elements of collation
- rys.; Bibliografia (na s.) - 13; Bibliografia (liczba pozycji) - 18; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 75
- Keywords in English
- poincare lemma, antiexact differential forms, homotopy operator, fermionic harmonic oscillator, complex manifold
- DOI
- DOI:10.1007/s00025-020-01247-8 Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s00025-020-01247-8 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 100
- Publication indicators
- = 1
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT776c76ed6faf47628ca52e34fbf998c0/
- URN
urn:pkr-prod:CUT776c76ed6faf47628ca52e34fbf998c0
* 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.