Geodesic
Quantization of weak gravitational waves in a closed Fridman model
Teoretičeskaâ i matematičeskaâ fizika, Tome 10 (1972) no. 3, pp. 399-411

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The problem of quantization of free tensor fields in a curved space-time is considered for the example of quantization of weak gravitational waves. The distinctive feature of quantization in a curved space-time is the violation of the homogeneity of time by the expansion of the Universe and the related nonconservation of energy. This last circumstance means that s is impossible to construct a “good” Hamiltonian. The problem can be resolved because of the spatiai homogeneity and the associated integral conservation law. 
@article{TMF_1972_10_3_a7,
     author = {A. A. Lyubushin},
     title = {Quantization of weak gravitational waves in a closed {Fridman} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {399--411},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_10_3_a7/}
}
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A. A. Lyubushin. Quantization of weak gravitational waves in a closed Fridman model. Teoretičeskaâ i matematičeskaâ fizika, Tome 10 (1972) no. 3, pp. 399-411. http://geodesic.mathdoc.fr/item/TMF_1972_10_3_a7/