Comment on formulating and generalizing Dirac's, Proca's, and Maxwell's equations with biquaternions or Clifford numbers

Details Comment on formulating and generalizing Dirac's, Proca's, and Maxwell's equations with biquaternions or Clifford numbers Comment on formulating and generalizing Dirac's, Proca's, and Maxwell's equations with biquaternions or Clifford numbers

2002-01-22

arxiv.org/abs/math-ph/0201049v1

Found.Phys.Lett. 14 (2001) 77-85

Physics

Mathematical Physics

8 pages, Dedicated to Freeman Dyson

Scientific paper

Many difficulties of interpretation met by contemporary researchers attempting to recast or generalize Dirac's, Proca's, or Maxwell's theories using biquaternions or Clifford numbers have been encountered long ago by a number of physicists including Lanczos, Proca, and Einstein. In the modern approach initiated by Gursey, these difficulties are solved by recognizing that most generalizations lead to theories describing superpositions of particles of different intrinsic spin and isospin, so that the correct interpretation emerges from the requirement of full Poincare covariance, including space and time reversal, as well as of reversion and gauge invariance. For instance, the doubling of the number of solutions implied by the simplest generalization of Dirac's equation (i.e., Lanczos's equation) can be interpreted as isospin. In this approach, biquaternions and Clifford numbers become powerful opportunities to formulate the Standard Model of elementary particles, as well as many of its possible generalizations, in very elegant and compact ways.

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