Operator calculus and invertible Clifford Appell systems: theory and application on the \(n\)-particle fermion algebra (Q2854015)

The authors investigate Appell systems in Clifford algebras with a general quadratic form. A system \(\left\{ \varphi _{0},\varphi _{1},\dots\right\} \) is called an Appell system with respect to an operator \( \mathcal{A}\) if \(\mathcal{A}^{n+1}\varphi _{n}=0\) and \(\varphi _{n}=\mathcal{ A}\varphi _{n-1}\) for all \(n\in \mathbb{N}\). The authors consider Clifford Appel systems with respect to lowering operators and Clifford multivectors. They develop methods for constructing invertible Appell systems. The paper extends the earlier work by the authors [Int. J. Pure Appl. Math. 31, No. 4, 427--446 (2006; Zbl 1136.15021)]. The paper has also a very good introduction which contains basic definitions and tools for the research topic. Motivations of the topic are evolution equations on Clifford algebras and the \(n\)-particle fermion algebra.