First we briefly describe the scalar fields on a two dimensional space-time
modeled as a standard (commutative) cylinder. Then we construct a noncommu
tative cylinder, a noncommutative generalization of a noncompact manifold.
Free scaler field on a noncommutative cylinder is investigated. Due to the
noncommutativity of the underlying space-time the energy frequencies are re
stricted, the time evolution is discrete. Within the perturbation theory th
is leads to an UV-regularization of Feynman diagrams. We expect that analog
ous properties will survive in a more realistic field theoretical models fo
rmulated on a noncommutative space-time.