Pauli algebra
From Encyclopedia of Mathematics
The 
-dimensional real Clifford algebra generated by the Pauli matrices [a1]
 |
where 
is the complex unit 
. The matrices 
, 
and 
satisfy 
and the anti-commutative relations:
 |
These matrices are used to describe angular momentum, spin-
fermions (which include the electron) and to describe isospin for the neutron, proton, mesons and other particles.
The angular momentum algebra is generated by elements 
satisfying
 |
 |
The Pauli matrices provide a non-trivial representation of the generators of this algebra. The correspondence
 |
leads to a realization of the quaternion division algebra (cf. also Quaternion) as a subring of the Pauli algebra. See [a2], [a3] for algebras with three anti-commuting elements.
References
| [a1] | W. Pauli, "Zur Quantenmechanik des magnetischen Elektrons" Z. f. Phys. , 43 (1927) pp. 601–623 |
| [a2] | Y. Ilamed, N. Salingaros, "Algebras with three anticommuting emements I: spinors and quaternions" J. Math. Phys. , 22 (1981) pp. 2091–2095 |
| [a3] | N. Salingaros, "Algebras with three anticommuting elements II" J. Math. Phys. , 22 (1881) pp. 2096–2100 |
How to Cite This Entry:
Pauli algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pauli_algebra&oldid=14443
Pauli algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pauli_algebra&oldid=14443
This article was adapted from an original article by G.P. Wene (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article