author={David Hestenes},
  journal={Journal of Mathematical Physics},
  • D. Hestenes
  • Published 1967
  • Physics
  • Journal of Mathematical Physics
The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (−1)½ which appears explicitly in the Dirac equation. In the modification of the Dirac electron theory which ensues, the (−1)½ appears as the generator of rotations in the spacelike plane orthogonal to the plane containing the electron current and spin vectors. This amounts to a further ``relativistic'' constraint on the spinor theory and so may be expected to have… 


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

Local observables in the Dirac theory

By a new method, the Dirac electron theory is completely reexpressed as a set of conservation laws and constitutive relations for local observables, describing the local distribution and flow of

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


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

Dirac Equation in the Clifford Algebra of Space

We translate the Dirac equation into the Clifford algebra of physical space. We study the second-order equation, the relativistic invariance, the gauge invariance, the Lagrangian density and the

Clifford Algebra and the Interpretation of Quantum Mechanics

The Dirac theory has a hidden geometric structure. This talk traces the conceptual steps taken to uncover that structure and points out significant implications for the interpretation of quantum

Covariant inertial forces for spinors

  • L. Fabbri
  • Physics
    The European Physical Journal C
  • 2018
In this paper we consider the Dirac spinor field in interaction with a background of electrodynamics and torsion-gravity; by performing the polar reduction we acquire the possibility to introduce a

On the Complementary Wave Interpretation of the Dirac Equation

The Dirac equation consistent with the principles of quantum mechanics and the special theory of relativity, introduces a set of matrices combined with the wave function of a particle in motion to

A Real Version of the Dirac Equation and Its Coupling to the Electromagnetic Field

A real version of the Dirac equation is derived and its coupling to the electromagnetic field considered. First the four-component real Majorana equation is briefly discussed. Then the complex Dirac

C ∗ Invariance of the Dirac Equation and Electromagnetism

In order to obtain a form invariance of the Dirac wave, the rel- ativistic quantum theory uses SL(2, C), a subset of the Clifford algebra C� 3 of the 3-dimensional physical space. In Dirac theory and



The quantum theory of the electron

The new quantum mechanics, when applied to the problem of the structure of the atom with point-charge electrons, does not give results in agreement with experiment. The discrepancies consist of

Space-time algebra

Preface to the Second Edition.- Introduction.- Part I:Geometric Algebra.- 1.Intrepretation of Clifford Algebra.- 2.Definition of Clifford Algebra.- 3.Inner and Outer Products.- 4.Structure of