Zz. Zhong, NONCOMMUTATIVE ANALYSIS, QUANTUM GROUP GAUGE TRANSFORMATIONS AND GAUGE-FIELDS, Journal of physics. A, mathematical and general, 26(8), 1993, pp. 391-399
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.