Evolution operators for linearly polarized two-Killing cosmological models

Abstract

We give a general procedure to obtain non perturbative evolution operators in closed form for quantized linearly polarized two Killing vector reductions of general relativity with a cosmological interpretation. We study the representation of these operators in Fock spaces and discuss in detail the conditions leading to unitary evolutions.

Exact Solutions for Time-Dependent Non-Hermitian Oscillators: Classical and Quantum Pictures

“…The profile of σ(t) and γ(t) is depicted in Figure 3, paying special attention to the constant mass Γ = 0 and Γ = 1 cases. In this figure, it is verified that the solution to the Ermakov equation is indeed always different from zero, as we stated earlier and proved in [8,9] (see also [65]). Therefore, the point transformation is non-singular for t ∈ R.…”

A Status Report on the Phenomenology of Black Holes in Loop Quantum Gravity: Evaporation, Tunneling to White Holes, Dark Matter and Gravitational Waves

“…In that case, the Hawking/LQG spectra could also be dicriminated for higher mass black holes [34]. This possibility is however extremely unlikely, and we will not discuss it further, as a damping in the pseudo-periodicity is expected to take place [37][38][39]. This analysis was pushed further in [40] where recent results are accounted for.…”

Quantization of Midisuperspace Models

“…In fact, the system can be described as a U (1) symmetric massless scalar field evolving in a fixed time-dependent 2+1 background (topologically R 2 × S 1 ) and with no extra constraints (at variance with the Gowdy T 3 case). The same unitarity problems that show up in the quantum evolution of the Gowdy models also appear here and can be solved again with a time dependent canonical transformation [21]. …”