Recently, some problems have been found in the definition of the partialderivative in the case of the presence of both explicit and implicit functionaldependencies in the classical analysis. In this talk we investigate theinfluence of this observation on the quantum mechanics and classical/quantumfield theory. Surprisingly, some commutators of the coordinate-dependentoperators are not equal to zero. Therefore, we try to provide mathematicalfoundations to the modern non-commutative theories. We also indicate possibleapplications in the Dirac-like theories.
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