CANONICAL QUANTIZATION OF D-DIMENSIONAL R2 GRAVITY

The canonical formalism of R2 gravity in spacetime of arbitrary dimension D > 4 is constructed. It is shown that there exist five qualitatively different forms of this theory, in each of which the constraints in the phase space are found. Canonical quantization in a unitary gauge is performed, and the generating functional of the Green's functions is represented as a functional integral over the original fields with local measure. It is shown that in four forms of the theory the local measure has a nonstandard form; moreover, the structure of the local measure in one of these forms has not hitherto been encountered in quantum field theory models.