# Clifford Algebra and the Interpretation of Quantum Mechanics

@inproceedings{Hestenes1986CliffordAA, title={Clifford Algebra and the Interpretation of Quantum Mechanics}, author={David Hestenes}, year={1986} }

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…

## 74 Citations

REAL DIRAC THEORY

- Physics
- 1996

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…

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- 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…

Geometric Algebra and Dirac Equation

- Mathematics, Physics
- 2006

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

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- 1990

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

- Physics
- 1990

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

- Mathematics
- 2019

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

- Physics
- 1993

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

- Physics
- 2007

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

- Mathematics
- 1993

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

- Physics
- 2009

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…

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