Complex q-Analysis and Scalar Field Theory on a q-Lattice
Abstract
We develop the basic formalism of complex q-analysis to study the solutions of second order q-difference equations which reduce, in the q→ 1 limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After defining an inner product on the function space we construct and study the properties of the solutions, and then apply this formalism to the Schr\"odinger equation and two-dimensional scalar field theory.
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