NONCOMMUTATIVE ANALYSIS, QUANTUM GROUP GAUGE TRANSFORMATIONS AND GAUGE-FIELDS

In this letter a non-commutative analytic method is given, we discuss what is a q-sequence, a q-analytic function, a q-derivative, a q-diffe rential equation and its solution, etc, respectively. By using these t erms the vector fields and the local quantum group GL(q)(2) gauge tran sformation on a quantum plane can be described. From the covariance re quirement under the gauge transformations we obtain the q-covariant de rivatives and the GL(q)(2) gauge field which is a quantum analogue of the GL(2) gauge field. The solutions of the GL(q)(2) gauge field equat ion are discussed, and the explicit form of the null gauge field solut ion is given.