We study scalar field theory in one space and one time dimensions on a q-deformed space with static background. We write the Lagrangian and the equation of motion and solve it to the first order in $q-1$ where $q$ is the deformation parameter of the space.
The Yukawa Model in One Space - One time Dimensions
Supersymmetry, p-brane duality and hidden space and time dimensions
Kink-boundary collisions in a two dimensional scalar field theory
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