Theory of fields in quantized spaces

It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4), O(3,3) or equivalent real forms of four-dimensional unitary algebras SU^*(4),SU(2,2),SL(4). The most surprising fact is that that all operations in the construction of such field theories are connected with compact manifolds. The gauge invariant theory in quantized space is proposed.