Canonical quantization of theories with higher derivatives. Quantization of $R^2$ gravitation

A generalization of Ostrogradsky's method for bringing theories with higher derivatives to the hamiltonian form is developed which is fit for applications to gauge fields theories. Hamiltonian formalism for the theory with the Lagrangian ${\mathcal L}=\sqrt{-g}(\Lambda -(1/\chi^2)R +aR_{\mu\nu} R^{\mu\nu} +bR^2)$ is formulated. Structure of constraints of this theory is investigated and it is shown that five essentially different variants of the theory are possible depending on the relationships between the parameters $\Lambda, \chi, a, b$. For all these variants canonical quantization is performed and local measure in the continual integral is found. The general form of the local measure is found for an arbitrary bosonic theory interacting with gravity.
${\mathcal L}=\sqrt{-g}(\Lambda -(1/\chi^2)R +aR_{\mu\nu} R^{\mu\nu} +bR^2)$. Исследована структура связей такой теории и показано, что в зависимости от соотношения между параметрами