•  44
    Electron paths, tunnelling, and diffraction in the spacetime algebra
    with Anthony Lasenby and Chris Doran
    Foundations of Physics 23 (10): 1329-1356. 1993.
    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 specifies a definite velocity, which might be interpreted as that of a real electron. Taken literally, this velocity yields predictions of tunnelling times through potential barriers, and defines streamlines in spacetime t…Read more
  •  42
    A multivector derivative approach to Lagrangian field theory
    with Anthony Lasenby and Chris Doran
    Foundations of Physics 23 (10): 1295-1327. 1993.
    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 and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-ener…Read more
  •  40
    States and operators in the spacetime algebra
    Foundations of Physics 23 (9): 1239-1264. 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 multivectors, and the quantum σ- and γ-matrices are replaced by two-sided multivector operations. The STA is defined over the reals, and the role of the scalar unit imaginary of quantum mechanics is played by a fixed spacetime bivector. The extension to multiparticle systems involves a separate copy of the STA…Read more
  •  62
    Imaginary numbers are not real—The geometric algebra of spacetime
    with Anthony Lasenby and Chris Doran
    Foundations of Physics 23 (9): 1175-1201. 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 numbers often used in conventional methods. Reflections and rotations are analyzed in terms of bilinear spinor transformations, and are then related to the theory of analytic functions and their natural extension in more th…Read more