Approximate canonical quantization for cosmological models (Q2710978)

The author presents an approximate quantization procedure of finite-dimensional, time-reparametrization invariant, nonintegrable systems. The presented method is based on the construction of a distinguished set of variables called Shanmugadhasan variables. In his procedure these variables are approximated to some order in the perturbation parameter which identifies the nonintegrable sector of the theory. Transforming then to new canonical variables the system under concern can be quantized using standard techniques. The author points out that his method has some similarities to the method developed by \textit{A. O. Barvinsky} [Classical Quantum Gravity 10, 1985-1999 (1993; Zbl 0801.47050)]and \textit{A. O. Barvinsky} and \textit{V. Krykhtin} [Classical Quantum Gravity 10, 1957-1984 (1993; Zbl 0802.47062)]. However, making use of the presented method the author proves the equivalence of Dirac's and the reduced methods of quantization up to arbitrary order in the perturbation parameter.