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2013•Infinite Dimensional Analysis Quantum Probability and Related TopicsRequires access

OPERATOR CALCULUS AND INVERTIBLE CLIFFORD APPELL SYSTEMS: THEORY AND APPLICATION TO THE n-PARTICLE FERMION ALGEBRA

René Schott, G. Stacey Staples

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Abstract

Motivated by evolution equations on Clifford algebras and illustrated with the n-particle fermion algebra, a theory of invertible left- and right-Appell systems is developed for Clifford algebras of an arbitrary quadratic form. This work extends and clarifies the authors' earlier work on Clifford Appell systems, operator calculus, and operator homology/cohomology. A direct connection is also shown between blade factorization algorithms and the construction of Appell systems in these algebras.

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Motivated by evolution equations on Clifford algebras and illustrated with the n-particle fermion algebra, a theory of invertible left- and right-Appell systems is developed for Clifford algebras of an arbitrary quadratic form. This work extends and clarifies the authors' earlier work on Clifford Appell systems, operator calculus, and operator homology/cohomology. A direct connection is also shown between blade factorization algorithms and the construction of Appell systems in these algebras.

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Available abstract

Motivated by evolution equations on Clifford algebras and illustrated with the n-particle fermion algebra, a theory of invertible left- and right-Appell systems is developed for Clifford algebras of an arbitrary quadratic form. This work extends and clarifies the authors' earlier work on Clifford Appell systems, operator calculus, and operator homology/cohomology. A direct connection is also shown between blade factorization algorithms and the construction of Appell systems in these algebras.

Key concepts: Clifford algebra, Mathematics, Algebra over a field, Classification of Clifford algebras, Invertible matrix, Clifford analysis, Cohomology, Connection (principal bundle)

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OPERATOR CALCULUS AND INVERTIBLE CLIFFORD APPELL SYSTEMS: THEORY AND APPLICATION TO THE n-PARTICLE FERMION ALGEBRA — Research Paper | ScholarLens