Method of solving conformal models in D-dimensional space I

We study the Hilbert space of conformal field theory in D-dimensional space. The latter is shown to have model-independent structure. The states of matter fields and gauge fields form orthogonal subspaces. The dynamical principle fixing the choice of model may be formulated either in each of these subspaces, or in their direct sum. In the latter case, gauge interactions are necessarily present in the model. We formulate the conditions specifying the class of models where gauge interactions are being neglected. The anomalous Ward identifies are derived. Different values of anomalous parameters (D-dimensional analogues of a central charge, including operator ones) correspond to different models. The structure of these models is analogous to that of 2-dimensional conformal theories. Each model is specified by D-dimensional analog of null vector. The exact solutions of the simplest models of this type are examined. It is shown that these models are equivalent to Lagrangian models of scalar fields with a triple interaction. The values of dimensions of such fields are calculated, and the closed sets of differential equations for higher Green functions are derived. (author). 25 refs