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 $q\to 1$ 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 Schrödinger equation and two-dimensional scalar field theory.

15 pages, LATEX, LTP-042-UPR

References in corpus (4)

• Representations of q-Minkowski space algebra
• A Model of Quantum Space-Time Symmetry in Two Dimensions
• Approach to Quantum Group deformed Quantum Field Theory
• Two-Dimensional Quantum PoincarÉ Group

Cited by in corpus (5)

• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Bose-Einstein condensation of a quantum group gas
• Thermodynamics of a free $S{U}_q(2)$ fermionic system
• Geometry of Quantum Group invariant systems
• Notes on Curtright-Zachos Deformations of osp(1,2) and Super Virasoro Algebras