NDLI: The Kähler-Dirac Equation with Non-Scalar-Valued Differential Form

Content Provider	Springer Nature Link
Author	Vargas, Jose G. Torr, Douglas G.
Copyright Year	2008
Abstract	The original, matrix-free Kähler-Dirac (KD) equation of 1960 has an unpleasant feature when the input differential form is not scalar-valued. Possibly to deal with that feature, Kähler proposed in 1962 a highly cumbersome alternative equation involving matrices. It coincides with the one from 1960 when the input differential form is scalar-valued.In the 5th Clifford Conference, we proposed our own alternative, where the tensor (1960) and matrix (1962) products of the valuedness factors were replaced with the Clifford product. We also suggested a sort of Kaluza-Klein (KK) space canonically determined by a subset of the fundamental invariants that define the spacetime manifold. In this paper we show that our KK space seems to accommodate the physics well for appropriate choice of the torsion. We further show that one can choose an input differential form highly appropriate for when the aforementioned torsion is assumed to be the output differential form of a geometrized KD equation. This leads to equations of structure for the torsion that have a more quantum-mechanical and less moving frame theory flavor than the standard ones.
Starting Page	1007
Ending Page	1021
Page Count	15
File Format	PDF
ISSN	01887009
Journal	Advances in Applied Clifford Algebras
Volume Number	18
Issue Number	3
e-ISSN	16614909
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2008-06-16
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Kähler Kähler-Dirac Kaluza-Klein Physics Applications of Mathematics Mathematical and Computational Physics Mathematical Methods in Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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