# New Foundations for Classical Mechanics

@inproceedings{Hestenes1986NewFF, title={New Foundations for Classical Mechanics}, author={David Hestenes}, year={1986} }

1: Origins of Geometric Algebra.- 1-1. Geometry as Physics.- 1-2. Number and Magnitude.- 1-3. Directed Numbers.- 1-4. The Inner Product.- 1-5. The Outer Product.- 1-6. Synthesis and Simplification.- 1-7. Axioms for Geometric Algebra.- 2: Developments in Geometric Algebra.- 2-1. Basic Identities and Definitions.- 2-2. The Algebra of a Euclidean Plane.- 2-3. The Algebra of Euclidean 3-Space.- 2-4. Directions, Projections and Angles.- 2-5. The Exponential Function.- 2-6. Analytic Geometry.- 2-7…

## 560 Citations

Relativistic Physics in theClifford Algebra Cℓ(1, 3)

- Mathematics
- 2009

There is growing evidence that the Clifford algebra C`(1, 3) is the appropriate mathematical structure to formulate physical theories. The geometries of 3-space and spacetime are naturally reflected…

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…

Part I: Vector Analysis of Spinors

- Mathematics, Physics
- 2015

Part I: The geometric algebra G3 of space is derived by extending the real number system to include three mutually anticommuting square roots of +1. The resulting geometric algebra is isomorphic to…

The Geometric Speed of Light

- 2004

This paper uses the Geometric Algebra (GA) on the Proper Time Geometry [1] to repeat Dirac's derivation of the Dirac equation from the Klein-Gordon equation. A GA is a type of Cli ord Algebra. These…

The Geometry of Fermions

- 2004

The Geometry of Fermions Carl Brannen (Dated: December 2, 2004) This paper analyzes the structure of the elementary fermions using the Geometric Algebras derived from several candidates for the…

Grassmann calculus, pseudoclassical mechanics, and geometric algebra

- Mathematics
- 1993

A reformulation of Grassmann calculus is presented in terms of geometric algebra—a unified language for physics based on Clifford algebra. In this reformulation, Grassmann generators are replaced by…

G8,2 Geometric Algebra, DCGA

- Mathematics
- 2015

The metric we use for G8;2 is (1; 1; 1; 1; i1; 1; 1; 1; 1; i1). This metric makes it very simple to use the CGA subalgebras of the CGA1 and CGA2 subspaces in a way fully compatible with CGA. These…

Volume-elements of integration: A geometric algebra approach

- Chemistry
- 2002

In this work, geometric algebra is applied to obtain the volume-element of integration for the 3 Cartesian coordinates of the center-of-mass, 3 Euler angles, and 3N−6 shape coordinates needed to…

Application of geometric algebra to theoretical molecular spectroscopy

- Mathematics
- 2001

In this work, geometric algebra has been applied to construct a general yet practical way to obtain molecular vibration-rotation kinetic energy operators, and related quantities, such as Jacobians.…

Geometrization of the physics with teleparallelism. II. Towards a fully geometric Dirac equation

- Physics
- 1992

In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of…