Multidimensional R ² gravity: the structure of constraints and canonical quantization

It is shown that curvature-squared gravity would be split into five essentially different variants at D)4. Every variant possesses its own number of physical degrees of freedom. The classification explicitly depends upon the dimension. The Dirac constrained canonical formalism is developed and its general structure is exhaustively studied. Explicit expressions of the first- and second-class constraints are specific for every variant of the theory.