Monthly Archives: January 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 3-dimensional space provides precise geometrical interpretations of the imaginary … Continued

We present a reformulation of Grassmann calculus in terms of geometric algebra – a unified language for physics based on Clifford algebra. In this reformulation, Grassmann generators are replaced by vectors, so that every product of generators has a natural … Continued

It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie group can be represented as a spin group. Thus, the computational power of geometric algebra is available to simplify the analysis and applications … Continued

This paper employs the ideas of geometric algebra to investigate the physical content of Dirac’s electron theory. The basis is Hestenes’ discovery of the geometric significance of the Dirac spinor, which now represents a Lorentz transformation in spacetime. This transformation … Continued

A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether’s theorem is found which is appropriate to both discrete … Continued

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 multivectors, and the quantum sigma- and gamma-matrices are replaced by two-sided multivector operations. The … Continued