1. For a discussion of the algebra of four-vectors, see E. Cartan, Theory of Spinors (Hermann, Paris, 1966) [Dover ed., N.Y., 1981 ]; A. O. Barut, Electrodynamics and Classical Theory of Fields and Particles ( Macmillan, N. Y., 1964 ).
2. M. A. Trump and W. C. Schieve, Found. Phys.
27, 1 (1997).
3. M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. II (Publish or Perish, Berkeley, 2nd ed. 1975 ).
4. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation ( Freeman, N. Y., 1973 ).
5. Cf. C. W. Misner, K. S. Thorne, and J. A. Wheeler, op. cit. footnote 20 on p. 75, where the acceleration of the particle is assumed to be constant. For constant acceleration, only two of the four directions of the co-moving basis are unique; the other two spacelike directions are arbitrary up to a spatial rotation. Here we have assumed the more general state of motion corresponding to a time-dependent acceleration particle.