A Classical Isodual Theory of Antimatter

An inspection of the contemporary physics literature reveals that, while matter is treated at all levels of study, from Newtonian mechanics to quantum field theory, antimatter is solely treated at the level of second quantization. For the purpose of initiating the restoration of full equivalence in the treatments of matter and antimatter in due time, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with expected images at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is anti–automorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also anti–automorphic, yet it is applicable beginning at the classical level and then persists at the quantum level. As part of our study, we present novel anti–isomorphic isodual images of the Galilean, special and general relativities and show the compatibility of their representation of antimatter with all available classical experimental knowledge, that on electromagnetic interactions. We also identify the prediction of antigravity for antimatter in the field of matter (or vice–versa) without any claim on its validity, and defer its resolution to specific experiments. To avoid a prohibitive length, the paper is restricted to the classical treatment which had not been sufficiently treated until now. Studies on operator profiles, such as the equivalence of isoduality and charge conjugation and the implication of the isodual theory in particle physics, are conducted n a separate paper.