Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras

Authors

Sultan Catto, CUNY Graduate CenterFollow
Yasemin Gürcan, CUNY Borough of Manhattan Community CollegeFollow
Amish Khalfan, CUNY La Guardia Community CollegeFollow
Levent Kurt, CUNY Borough of Manhattan Community CollegeFollow
V. Kato La, Columbia University

Document Type

Article

Publication Date

2016

Abstract

We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.

Comments

This article was originally published in the Journal of Physics: Conference Series 766 (2016) 012001. doi:10.1088/1742-6596/766/1/012001.