  We present a systematic organization of functions and operators on the fuzzy
2-sphere in terms of string modes, which are optimally localized in position
and momentum space. This allows to separate the semi-classical and the deep
quantum regime of non-commutative quantum field theory and exhibits its
nonlocal nature. This organization greatly simplifies the computation of loop
contributions, avoiding oscillatory integrals and providing the effective
action directly in position space. UV/IR mixing is understood as nonlocality
arising from long string modes in the loops. The method is suited for any
quantized symplectic space.
