Does antimatter emit a new light ?

We identify a number of problematic aspects of current classical and quantum theories of antimatter; we introduce a new mathematical formalism which is an antiautomorphic image of that of matter equivalent to charge conjugation at the operator level, but applicable from Newton's equations to quantum mechanics; we show that the emerging new theory of antimatter recovers known experimental data on electroweak interactions; we finally identity the following predictions of the theory: 1) reversal in the field of matter of the gravitational curvature (antigravity) for stable antiparticles and their bound states, such as the anti-hydrogen atom; 2) conventional (attractive) gravity for a bound state of an elementary particle and its antiparticle, such as the positronium; and 3) prediction that the anti- hydrogen atom emits a new photon which coincides with the conventional photon for all electroweak interactions but experiences repulsion in the gravitational field of matter.Comment: 18 pages, TEX, in press at Hyperfine Inte

Representations of the cyclically symmetric q-deformed algebra soq(3)so_q(3)

An algebra homomorphism $\psi$ from the nonstandard q-deformed (cyclically symmetric) algebra $U_q(so_3)$ to the extension ${\hat U}_q(sl_2)$ of the Hopf algebra $U_q(sl_2)$ is constructed. Not all irreducible representations of $U_q(sl_2)$ can be extended to representations of ${\hat U}_q(sl_2)$. Composing the homomorphism $\psi$ with irreducible representations of ${\hat U}_q(sl_2)$ we obtain representations of $U_q(so_3)$. Not all of these representations of $U_q(so_3)$ are irreducible. Reducible representations of $U_q(so_3)$ are decomposed into irreducible components. In this way we obtain all irreducible representations of $U_q(so_3)$ when $q$ is not a root of unity. A part of these representations turns into irreducible representations of the Lie algebra so$_3$ when $q\to 1$. Representations of the other part have no classical analogue. Using the homomorphism $\psi$ it is shown how to construct tensor products of finite dimensional representations of $U_q(so_3)$. Irreducible representations of $U_q(so_3)$ when $q$ is a root of unity are constructed. Part of them are obtained from irreducible representations of ${\hat U}_q(sl_2)$ by means of the homomorphism $\psi$.Comment: 28 pages, LaTe