  Some ambiguities have recently been found in the definition of the partial
derivative (in the case of presence of both explicit and implicit dependencies
of the function subjected to differentiation). We investigate the possible
influence of this subject on quantum mechanics and the classical/quantum field
theory. Surprisingly, some commutators of operators of space-time 4-coordinates
and those of 4-momenta are {\it not} equal to zero. We postulate the
non-commutativity of 4-momenta and we derive mass splitting in the Dirac
equation. Moreover, two iterated limits may not commute each other, in general.
Thus, we present an example when the massless limit of the function of $E, {\bf
p}, m$ does not exist in some calculations within quantum field theory.
KEYWORDS: Non-commutativity, quantum mechanics, whole-partial derivatives.
PACS: 04.62.+v 02.40.Gh 02.30.-f
