Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras

International Conference on Quantum Science and Applications 2016

Catto, Sultan^1,2 ; Gürcan, Yasemin^3 ; Khalfan, Amish^4 ; Kurt, Levent^3 ; La, V. Kato^5

Physics Department, Graduate School, City University of New York, New York

NY

10016-4309, United States^1

Theoretical Physics Group, Rockefeller University, 1230 York Avenue, New York

NY

10021-6399, United States^2

Department of Science, Borough of Manhattan CC, City University of NY, New York

NY

10007, United States^3

Physics Department, LaGuardia CC, City University of New York, LIC, NY

11101, United States^4

Columbia University, New York

NY

10027, United States^5

关键词: Arbitrary dimension;    Clifford algebra;    Construction scheme;    Fermi-Dirac statistics;    Heisenberg algebras;    Hermitian conjugate;    Identity matrices;    Linear combinations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/766/1/012001/pdf
DOI  :  10.1088/1742-6596/766/1/012001

来源: IOP

【 摘 要 】

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.