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  • 1995-1999  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    Dirac-Hestenes Lagrangian (1999)
    Springer
    International journal of theoretical physics 38 (1999), S. 2349-2369 
    Details
    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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  • 2
    Electronic Resource
    Electronic Resource
    Complex Geometry and Dirac Equation (1998)
    Springer
    International journal of theoretical physics 37 (1998), S. 2415-2431 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit $$i = \sqrt { - 1} $$ . We discuss two possibilities which appearin the multivector algebra approach: theσ123 and σ21 complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit $$i = \sqrt { - 1} $$ is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026675210893
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    Paper (German National Licenses)
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