C-statistical quantum groups and Weyl algebras

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Abstract
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.