Comment on `Dirac theory in spacetime algebra'

@article{Baylis2002CommentO,
  title={Comment on `Dirac theory in spacetime algebra'},
  author={William E. Baylis},
  journal={Journal of Physics A},
  year={2002},
  volume={35},
  pages={4791-4796}
}
  • W. E. Baylis
  • Published 11 February 2002
  • Physics
  • Journal of Physics A
In contrast to formulations of the Dirac theory by Hestenes and by the present author, the formulation recently presented by Joyce (Joyce W P 2001 J. Phys. A: Math. Gen. 34 1991-2005) is equivalent to the usual Dirac equation only in the case of vanishing mass. For nonzero mass, solutions to Joyce's equation can be solutions either of the Dirac equation in the Hestenes form or of the same equation with the sign of the mass reversed, and in general they are mixtures of the two possibilities… 

COMMENT: Reply to Comment on `Dirac theory in spacetime algebra'

The Dirac theory formulated by Joyce (Joyce W P 2001 J. Phys. A: Math. Gen. 34 1991-2005) is equivalent to two copies of the usual Dirac formulation. The comment of Baylis (Baylis W E 2002 J. Phys.

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References

SHOWING 1-10 OF 26 REFERENCES

REAL DIRAC THEORY

The Dirac theory is completely reformulated in terms of Spacetime Algebra, a real Clifford Algebra characterizing the geometrical properties of spacetime. This eliminates redundancy in the

Dirac theory in spacetime algebra: I. The generalized bivector Dirac equation

This paper formulates the standard Dirac theory without resorting to spinor fields. Spinor fields mix bivectors and vectors which have different properties in spacetime algebra. Instead the Dirac

Classical eigenspinors and the Dirac equation.

  • Baylis
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1992
TLDR
The four-velocity and orientation of an «elementary» particle is given classically by the Lorentz transformation, which is the classical eigenspinor of the particle; it is shown to satisfy a trivial four-momentum relation that is the exact analog of the Dirac equation of relativistic quantum theory.

Observables, operators, and complex numbers in the Dirac theory

The geometrical formulation of the Dirac theory with spacetime algebra is shown to be equivalent to the usual matrix formalism. Imaginary numbers in the Dirac theory are shown to be related to the

GEOMETRY OF THE DIRAC THEORY

The Dirac wave function is represented in a form where all its components have obvious geometrical and physical interpretations. Six components compose a Lorentz transformation determining the

Spacetime Algebra and Electron Physics

Comment on Formulating and Generalizing Dirac's, Proca's, and Maxwell's Equations with Biquaternions or Clifford Numbers

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

Clifford (Geometric) Algebras: With Applications to Physics, Mathematics, and Engineering

History of Clifford algebras teaching Clifford algebras operator approach to spinors flags, poles and dipoles introduction to geometric algebras linear transformations directed integration linear

New forms of the Dirac equation

SummaryA new form of the Dirac equation is derived, in which the wave function is a 2 × 2 matrix, rather than a 4-component column vector (or bispinor). The matrix has a simple physical

On a conform-invariant spinor wave equation

SummaryAs a possible basis for a unitary description of particles a new spinor wave equation is proposed which is similar to Heisenberg’s non-linear generalization of Dirac’s equation but exhibits in