Three examples of quantum dynamics on the half-line with smooth bouncing

Almeida, Carla Rodrigues; Bergeron, Hervé; Gazeau, Jean‐Pierre; Scardua, Arthur C.

doi:10.48550/arxiv.1708.06422

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“…The latter is essential for our approach to quantum cosmology [23, 24, Bergeron-etal1(2015), Bergeron-etal2(2016)] described below. A pedagogical presentation of the procedure is found in [25]. See also [26] for an interesting application to the quantum Brans-Dicke model.…”

Section: Integral Quantizationmentioning

confidence: 99%

“…In analogy to the Weyl-Heisenberg group for the full plane, we adopt the so-called covariant affine group quantization (see for instance [20] or a pedagogical presentation [21]) of functions of the isotropic variables (q, p) belonging to the half-plane R * + × R. This quantization is consistent with the symmetry of the half-plane corresponding to the arbitrariness of the choice of the origin, namely 1 for the scaling variable q and 0 for its conjugate momentum p. The respective phase space transformations form the affine group Aff + (R) of the real line, that is,…”

Section: Quantization Of the Isotropymentioning

confidence: 99%

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Quantum Mixmaster as a Model of the Primordial Universe

et al. 2019

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The Mixmaster solution to Einstein field equations was examined by C. Misner in an effort to better understand the dynamics of the early universe. We highlight the importance of the quantum version of this model for early universe. This quantum version and its semi-classical portraits are yielded through affine and standard coherent state quantizations and more generally affine and Weyl-Heisenberg covariant integral quantizations. The adiabatic and vibronic approximations widely used in molecular physics can be employed to qualitatively study the dynamics of the model on both quantum and semi-classical levels. Moreover, the semi-classical approach with the exact anisotropy potential can be effective in numerical integration of some solutions. Some promising physical features such as the singularity resolution, smooth bouncing, the excitation of anisotropic oscillations and a substantial amount of post-bounce inflation as the backreaction to the latter are pointed out. Finally, a realistic cosmological scenario based on the quantum mixmaster model, which includes the formation and evolution of local structures is outlined.

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Section: Integral Quantizationmentioning

confidence: 99%

Section: Quantization Of the Isotropymentioning

confidence: 99%