ISSN:
1572-9575
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We formulate the variational principle of theDirac equation within the noncommutative even space-timesubalgebra, the Clifford $$\mathbb{R}$$ -algebra $${Cl_{_{1,3} }^ + }$$ . A fundamental ingredient in ourmultivectorial algebraic formulation is a $$\mathbb{D}$$ -complex geometry, $$\mathbb{D} \equiv {span}_\mathbb{D} \left\{ {1,{\gamma }_{{21}} } \right\},{\gamma }_{{21}} \in Cl_{_{1,3} }^ +$$ . We derive the Lagrangian for theDirac-Hestenes equation and show that it must be mapped on $$\mathbb{D}\; \otimes \;\mathcal{F}$$ , where ℱ denotes an $$\mathbb{R}$$ -algebra of functions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1026627819148
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