Geodesic
Nonconformal Scalar Field in a Homogeneous Isotropic Space and the Hamiltonian Diagonalization Method
Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 1, pp. 115-124

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We diagonalize the metric Hamiltonian and evaluate the energy spectrum of the corresponding quasiparticles for a scalar field coupled to a curvature in the case of an $N$-dimensional homogeneous isotropic space. The energy spectrum for the quasiparticles corresponding to the diagonal form of the canonical Hamiltonian is also evaluated. We construct a modified energy-momentum tensor with the following properties: for the conformal scalar field, it coincides with the metric energy-momentum tensor; the energies of the particles corresponding to its diagonal form are equal to the oscillator frequency; and the number of such particles created in a nonstationary metric is finite. We show that the Hamiltonian defined by the modified energy-momentum tensor can be obtained as the canonical Hamiltonian under a certain choice of variables. 
@article{TMF_2001_126_1_a4,
     author = {Yu. V. Pavlov},
     title = {Nonconformal {Scalar} {Field} in a {Homogeneous} {Isotropic} {Space} and the {Hamiltonian} {Diagonalization} {Method}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {115--124},
     publisher = {mathdoc},
     volume = {126},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_126_1_a4/}
}
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Yu. V. Pavlov. Nonconformal Scalar Field in a Homogeneous Isotropic Space and the Hamiltonian Diagonalization Method. Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 1, pp. 115-124. http://geodesic.mathdoc.fr/item/TMF_2001_126_1_a4/