An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain types of Finsler space, (...) and a derivation of a Kaluza-Klein type metric. Frame transport in general Riemannian space-time is also discussed. (shrink)

A model of the extended classical charged particle is developed further to prove that the electron potential can be expressed as a superposition of null waves. The null waves are solutions of the homogeneous wave equation and are related to some recently discovered types of solutions which are localized and propagate without dispersion. Connections with quantum electrodynamics and the fine structure constant are indicated.

Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.

A recently developed formalism which gives a unified picture of the linear transport of moving frames is extended to include a particular type of transport under the 10-parameter Poincaré group. The frame coordinates are expressed in a 5 × 5 matrix representation which includes the position four-vector plus orthonormal tetrads for the internal coordinates. This provides a general description of the kinematics of physical systems which can be represented by moving frames. Several examples are given, including systems moving with spin (...) and Zitterbewegung along both timelike and null paths. The concept of boost or Poincaré momentum is related to system kinematics. Lagrangians of these systems are also discussed. (shrink)

A theory of the extended classical charged particle is presented. The theory assumes extension along the forward light cone of the particle instead of the usual now-plane. Solutions are given for many of the traditional problems including 4/3, instability, infinite self-energy, and runaway velocity. The Lorentz and Lorentz-Dirac equations are derived from a more general equation of motion.