Geodesic
Quantized scalar field in Friedmann–Lobachevskii space
Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 2, pp. 226-234
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A quantized scalar field is considered in an open Friedmann universe wich a Lorentz invariant spatial part. Since the Friedmann universe is nomstationary, the energy of a free field is a not conserved and the Hamiltonian is not diagonal in the creation and annihilation operators. The Hamiltonian is diagonaliized by means of a set of $\eta$-dependent representations ($\eta$ is the time) of the commutation relations with Lorentz invariant vacuum states. The $\eta$-wacuum mean value of the operator of the number density of particles corresponding to the $\eta_0$ representation ($\eta>\eta_0$) is caleulated. The question of $\eta$ a quasielassieal limit is discussed and a transition is made to flat space-time. 
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B. A. Levitskii. Quantized scalar field in Friedmann–Lobachevskii space. Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 2, pp. 226-234. http://geodesic.mathdoc.fr/item/TMF_1971_8_2_a6/

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