# 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} }

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…

## 13 Citations

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

- Physics
- 2002

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.…

### Dirac Theory in Euclidean 3D Geometric Algebra (Cl3)

- Physics
- 2020

This article is intended as an addition to the book [10], since, in the first edition, I was double minded whether to introduce the Dirac theory for young students. Now I am quite sure that it should…

### Discrete Dirac-Kähler equation and its formulation in algebraic form

- Mathematics
- 2016

A relationship between the discrete Dirac-Kahler equation and discrete analogues of some Dirac type equations in the geometric spacetime algebra is discussed. We show that a solution of the discrete…

### Spinors, Gauges, Geometric Algebra, and Probabilities

- Mathematics
- 2006

Recent advances[1] in Bohmian mechanics suggest that quantum mechanics should consider the density matrix as the fundamental quantum object rather than the spinor wave state. This change allows a…

### Equivalence of Dirac formulations

- Mathematics, Physics
- 2002

We construct general Dirac theories in both ⊗ l(3, 1) and ⊗ l(1, 3) using a first order left acting Dirac operator. Any two such theories are equivalent provided they have the same dimension. We also…

### A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form

- Mathematics
- 2019

We construct a discrete version of the plane wave solution to a discrete Dirac-Kähler equation in the Joyce form. A geometric discretisation scheme based on both forward and backward difference…

### Discrete versions of some Dirac type equations and plane wave solutions

- Mathematics
- 2017

A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution…

### A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme

- MathematicsAdvances in Applied Clifford Algebras
- 2018

Discrete models of the Dirac–Kähler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation…

### Discrete Dirac-K\"ahler and Hestenes equations

- Mathematics
- 2015

A discrete analogue of the Dirac equation in the Hestenes form is constructed by introduction the Clifford product on the space of discrete forms. We discuss the relation between the discrete…

### Quaternions in mathematical physics (2): Analytical bibliography

- Physics
- 2005

This is part two of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1-Alphabetical bibliography , 2-Analytical bibliography,…

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