C-STATISTICAL QUANTUM GROUPS AND WEYL ALGEBRAS

C-statistical quantum groups and algebras are obtained by a process of transmutation. They are like super-quantum groups and algebras but with statistics given now by a complex number. Among the examples, it is shown that the Weyl algebra of canonical quantization may be viewed equivalently as a C-statistical plane. Related examples are the "noncommutative torus" and a double loop-variable quantization of photons. These results lead toward a reformulation of ordinary quantum mechanics as a classical theory with C-statistics. In this reformulation, the role of the +/- 1 factors of super statistics is played by the free-particle time evolution.