Clifford Algebra and the Interpretation of Quantum Mechanics

  title={Clifford Algebra and the Interpretation of Quantum Mechanics},
  author={David Hestenes},
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 mechanics. The unit imaginary in the Dirac equation is shown to represent the generator of rotations in a spacelike plane related to the spin. This implies a geometric interpretation for the generator of electromagnetic gauge transformations as well as for the entire electroweak gauge group of the… 
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
Geometry of spin ½ particles
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
Geometric Algebra and Dirac Equation
Geometric algebra (a geometrical interpretation of Clifford algebras) is an alternative to vector calculus that is designed to give more geometric meaning to the formalisms used in physics. We
On Decoupling Probability from Kinematics in Quantum Mechanics
A means for separating subjective and objective aspects of the electron wave function is suggested, based on a reformulation of the Dirac Theory in terms of Spacetime Algebra. The reformulation
The zitterbewegung interpretation of quantum mechanics
Thezitterbewegung is a local circulatory motion of the electron presumed to be the basis of the electron spin and magnetic moment. A reformulation of the Dirac theory shows that thezitterbewegung
On Computable Geometric Expressions in Quantum Theory
Geometric Algebra and Calculus are mathematical languages that encode fundamental geometric relations that theories of physics must respect, and eliminate from our vocabulary those they do not. We
States and operators in the spacetime algebra
The spacetime algebra (STA) is the natural, representation-free language for Dirac's theory of the electron. Conventional Pauli, Dirac, Weyl, and Majorana spinors are replaced by spacetime
Dirac ' s theory in real geometric formalism : multivectors versus spinorsJosep
A fully classical real vector reformulation of Dirac's equation is developed from scratch. It is then shown to be almost equivalent to the Hestenes-Dirac equation when formulated in terms of
Imaginary numbers are not real—The geometric algebra of spacetime
This paper contains a tutorial introduction to the ideas of geometric algebra, concentrating on its physical applications. We show how the definition of a “geometric product” of vectors in 2-and
The mystery of square root of minus one in quantum mechanics, and its demystification
To most physicists, quantum mechanics must embrace the imaginary number i = square root of minus one is at least a common belief if not a mystery. We use the famous example pq -qp = h/(2 pi i) to


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
Space-time structure of weak and electromagnetic interactions
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
Quantum mechanics from self-interaction
We explore the possibility thatzitterbewegung is the key to a complete understanding of the Dirac theory of electrons. We note that a literal interpretation of thezitterbewegung implies that 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
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
  • Mate. (Roma) Ser. V, 21, 425
  • 1962
  • C. Ross
  • Medicine
    The Dental register
  • 1869
Geometric Calculus and Elementary Particles.
Scalar products of spinors and an extension of Brauer-Wall groups
The automorphism groups of scalar products of spinors are determined. Spinors are considered as elements of minimal left ideals of Clifford algebras on quadratic modules, e.g., on orthogonal spaces.
Rend. Mate. (Roma) Ser. V
  • Rend. Mate. (Roma) Ser. V
  • 1962