Publication details

The Poincare Lemma, Antiexact Forms, and Fermionic Quantum Harmonic Oscillator

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KYCIA Radoslaw Antoni

Year of publication 2020
Type Article in Periodical
Magazine / Source Results in Mathematics
MU Faculty or unit

Faculty of Science

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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