Andre Unterberger, University of Reims, France

Applying relativistic quantization to special function theory


This is the beginning of a two-column dictionary: relativistic mathematics on the right, non-relativistic special case c=\infty on the left. Starting from the relativistic oscillator (the concept corresponding to the harmonic oscillator from non-relativistic theory), one brings to light, in a coherent way, Mathieu functions as well as confluent Heun functions. Some new formulas are obtained with the help of the Klein-Gordon calculus, a relativistic substitute for the Weyl calculus introduced and developedby the applicant.