Abstract :
Over the past sixty years many attempts have been made at modifying quantum mechanics by extending the field of complex numbers, but none has led to a structural unification of quantum mechanics with relativity. A solution nevertheless exists. It is based on a ring, new to mathematics, which we call the quantal ring. It is manifestly Lorentz covariant, CPT invariant, contains the field of complex numbers as a substructure, and is free of properties that have no physical interpretation. While the systematic derivation of this ring from a comparative abstract analysis of classical and quantum mechanics, as well as the proof of its uniqueness and the construction of a generalized Hilbert space over it, are being finalized for publication, we derive it in this note by a simple alternative construction.
