The Poincare Lemma, Antiexact Forms, and Fermionic Quantum Harmonic Oscillator
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Results in Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1007/s00025-020-01247-8 |
| Doi | http://dx.doi.org/10.1007/s00025-020-01247-8 |
| Keywords | Poincare lemma; antiexact differential forms; homotopy operator; fermionic harmonic oscillator; complex manifold |
| Description | The paper focuses on various properties and applications of the homotopy operator, which occurs in the Poincare lemma. In the first part, an abstract operator calculus is constructed, where the exterior derivative is an abstract derivative and the homotopy operator plays the role of an abstract integral. This operator calculus can be used to formulate abstract differential equations. An example of the eigenvalue problem that resembles the fermionic quantum harmonic oscillator is presented. The second part presents the dual complex to the Dolbeault bicomplex generated by the homotopy operator on complex manifolds. |
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