# GEOMETRY OF THE DIRAC THEORY

@inproceedings{Hestenes1998GEOMETRYOT, title={GEOMETRY OF THE DIRAC THEORY}, author={David Hestenes}, year={1998} }

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 electron velocity are spin directions. This provides the basis for a rigorous connection between relativistic rigid body dynamics and the time evolution of the wave function. The scattering matrix is given a new form as a spinor-valued operator rather than a complex function. The approach reveals a…

## Tables from this paper

## 14 Citations

### Electron Scattering without Spin Sums

- Physics
- 2001

Using the spacetime algebra formulation of the Dirac equation, we demonstrate how to perform cross-section calculations following a method suggested by Hestenes (1982). Instead of an S-matrix, we use…

### Geometry of spin ½ particles

- Physics
- 2015

The geometric algebras of space and spacetime are derived by sucessively extending the real number system to include new mutually anticommuting square roots of ±1. The quantum mechanics of spin 1/2…

### Comment on `Dirac theory in spacetime algebra'

- Physics
- 2002

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…

### 20 02 Comments on “ Dirac theory in spacetime algebra ”

- Physics
- 2001

In contrast to formulations of the Dirac theory by Hestenes and by the current author, the formulation recently presented by W. P. Joyce [J. Phys. A: Math. Gen. 34 (2001) 1991–2005] is equivalent to…

### Algebra of Complex Vectors and Applications in Electromagnetic Theory and Quantum Mechanics

- Mathematics
- 2015

A complex vector is a sum of a vector and a bivector and forms a natural extension of a vector. The complex vectors have certain special geometric properties and considered as algebraic entities.…

### Neoclassical theory of elementary charges with spin of 1/2

- Physics
- 2014

We advance here our neoclassical theory of elementary charges by integrating into it the concept of spin of 1/2. The developed spinorial version of our theory has many important features identical to…

### Properties of a Possible Unification Algebra

- MathematicsSSRN Electronic Journal
- 2022

An algebra providing a possible basis for the standard model is presented. The algebra is generated by combining the trigintaduonion Cayley-Dickson algebra with the complexified space-time Clifford…

### Some Paradoxes in Special Relativity and the Resolutions

- Physics, Philosophy
- 2011

The special theory of relativity is the foundation of modern physics, but its unusual postulate of invariant vacuum speed of light results in a number of plausible paradoxes. This situation leads to…

### THE FORCE OF GRAVITY IN SCHWARZSCHILD AND GULLSTRAND–PAINLEVÉ COORDINATES

- Physics
- 2009

We derive the exact equations of motion (in Newtonian, F = ma, form) for test masses in Schwarzschild and Gullstrand–Painleve coordinates. These equations of motion are simpler than the usual…

## References

SHOWING 1-10 OF 15 REFERENCES

### Local observables in the Dirac theory

- Physics
- 1973

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

- Physics
- 1975

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…

### REAL SPINOR FIELDS.

- Physics
- 1967

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…

### Spin and uncertainty in the interpretation of quantum mechanics

- Physics
- 1979

A rigorous derivation of the Schrodinger theory from the Pauli (or Dirac) theory implies that the Schrodinger equation describes an electron in an eigenstate of spin. Furthermore, the ground‐state…

### Consistency in the formulation of the Dirac, Pauli, and Schrödinger theories

- Physics
- 1975

Properties of observables in the Pauli and Schrodinger theories and first order relativistic approximations to them are derived from the Dirac theory. They are found to be inconsistent with customary…

### Space-time structure of weak and electromagnetic interactions

- Mathematics
- 1982

The generator of electromagnetic gauge transformations in the Dirac equation has a unique geometric interpretation and a unique extension to the generators of the gauge group SU(2) × U(1) for the…

### Polarization of Spin-1/2 Particles in Scattering Processes

- Physics
- 1972

For a beam of spin-12 particles with definite momentum, a complete description of the spin state is provided by a single three-space vector, the polarization. This paper shows how the…

### Proper dynamics of a rigid point particle

- Physics
- 1974

A spinor formulation of the classical Lorentz force is given which describes the precession of an electron's spin as well as its velocity. Solutions are worked out applicable to an electron in a…

### Proper particle mechanics

- Physics
- 1974

Spacetime algebra is employed to formulate classical relativistic mechanics without coordinates. Observers are treated on the same footing as other physical systems. The kinematics of a rigid body…

### Space-time algebra

- Mathematics, Physics
- 1966

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…