The travelling wave group is a solution to the wave equation. With a Gaussian envelope, this stable wave does not spread as it propagates. The group is derived for electromagnetic waves and converted with Planck’s law to quantized photons. The resulting wave is a probability amplitude, and this is adapted to particles subject to special relativity. By including mass and by inverting the wave group, a description for antiparticles is derived. The consequent explanation is consistent with Dirac’s relativistic equation and with his theory of the electron; while being more specific than his idea of the wave packet, and more stable. The travelling wave group is extended to describe the positron, either free or in an external field.
Cite this paper
A. Bourdillon, "A Travelling Wave Group II: Antiparticles in a Force Field," Journal of Modern Physics, Vol. 4 No. 6, 2013, pp. 705-711. doi: 10.4236/jmp.2013.46097.
 A. Einstein, B. Podolski and N. Rosen, Physical Review, Vol. 47, 1935, pp. 777-780.
 N. Bohr, “The Philosophical Writings of Niels Bohr, Vols I, II, and III,” Ox Bow Press, Woodbridge, 1987.
 A. J. Bourdillon, Journal of Modern Physics, Vol. 3, 2012, pp. 290-296.
 J. M. Ziman, “Elements of Advanced Quantum Theory,” Cambridge University Press, Cambridge, 1969.
 P. A. M. Dirac, “The Principles of Quantum Mechanics,” 4th Edition, Clarendon Press, 1958.
 I. A. Arbab, Journal of Modern Physics, Vol. 2, 2011, pp. 1012-1016. doi:10.4236/jmp.2011.29121
 J. Longdell, Nature, Vol. 469, 2011, pp. 475-476.
 J. S. Bell, Reviews of Modern Physics, Vol. 38, 1966, pp. 447-452. doi:10.1103/RevModPhys.38.447
 D. Bohm and J. Bub, Reviews of Modern Physics, Vol. 38, 1966, pp. 453-475. doi:10.1103/RevModPhys.38.453