Realization, Classification, and Extension of Certain Physically Important Groups and Algebras
Oct, 197935 pages
Published in:
- J.Math.Phys. 22 (1981) 226
DOI:
Report number:
- Print-79-0895 (MASS.U.,BOSTON)
View in:
Citations per year
Abstract: (AIP)
An associative algebra of differential forms with division has been constructed. The algebra of forms in each different space provides a practical realization of the universal Clifford algebra of that space. A classification of all such algebras is given in terms of two distinct types of algebrasN k and S k . The former include the dihedral, quaternion, and Majorana algebras; the latter include the complex, spinor, and Diracalgebras. The associative product expresses Hodge duality as multiplication by a basis element. This makes possible the realization of higher order algebras in a calculationally useful algebraic setting. The fact that the associative algebras, as well as the enveloped Lie algebras, are precisely those arising in physics suggests that this formalism may be a convenient setting for the formulation of basic physical laws.- GROUP THEORY: DUALITY
- ALGEBRA: CLIFFORD
- ALGEBRA: QUATERNION
- ALGEBRA: MAJORANA
- ALGEBRA: SPINOR
- SPINOR: ALGEBRA
- ALGEBRA: DIRAC
- ALGEBRA: LIE
- ALGEBRA: JORDAN
References(13)
Figures(0)