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