MULTIDIMENSIONAL R2 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. However, the algebra of first-class constraints has the same conventional form in each variant. The canonical quantization is carried out by the path integral formalism on the basis of the constrained Hamiltonian formalism developed. The covariant path integral over the metric is obtained from the consistent canonical quantization. The non-trivial local measure of covariant path integration has a form which is specific for every theory variant and depends manifestly upon the space dimension.