Complex $q$-Analysis and Scalar Field Theory on a $q$-Lattice

Details Complex $q$-Analysis and Scalar Field Theory on a $q$-Lattice Complex $q$-Analysis and Scalar Field Theory on a $q$-Lattice

1994-02-22

arxiv.org/abs/hep-th/9402124v1

Mod.Phys.Lett.A9:1121-1130,1994

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LATEX, LTP-042-UPR

Scientific paper

10.1142/S0217732394000939

We develop the basic formalism of complex $q$-analysis to study the solutions of second order $q$-difference equations which reduce, in the $q\rightarrow 1$ 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\"{o}dinger equation and two-dimensional scalar field theory.

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