General quantization

One can convert a singular physical theory of several levels based on Lie algebras into a regular one with nearly the same finite predictions and symmetries in a limited correspondence domain by a routine general quantization: 1. Simplify the algebra of each level by a small homotopy, adducing as few new variables as possible, and respecting the relation between levels. 2. Represent the resulting algebras by finite matrices approximating the singular theory in the correspondence domain. This procedure extends and unifies those of special relativization, general relativization, and canonical quantization. For exercise I general-quantize the scalar meson field in Minkowski space-time. The first-level quantization that simplifies the Poincaré algebra also curves, quantizes, and unifies space-time, a complex plane, and momentum-energy, into a quantum space composed of quantum processes with group SO(5, 1) and bosonic statistics. A second-level quantization that simplifies the field algebra then yields a finite relativistic quantum dynamical theory whose quanta have nearly bosonic statistics. Two small quantum constants besides ~ and 1/c2 define the simplification, and three large quantum numbers l1 ≫ l2, l3 ≫ 1 define the representation.