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Quantum cosmology: mathematics times physics. (English) Zbl 1459.83072

Summary: We mention, in general terms, the basic ideas of quantum cosmology (QC) and how such framework can be intertwined with General Relativity (GR). The author aimed to be less technical and focus more on introducing in simple terms some concepts [Quantum cosmology – the supersymmetric perspective. Vol. 1: Fundamentals. Berlin: Springer (2010; Zbl 1219.83004); Quantum cosmology – the supersymmetric perspective. Vol. 2: Advanced topics. Berlin: Springer (2010; Zbl 1219.83005)]. In order to present new advances that may be of interest to readers, we very briefly discuss recent results involving hidden symmetries, showing that specific boundary conditions can be related to the algebra of Dirac observables afterwards associated to the algebra of supersymmetry [loc. cit.].

MSC:

83F05 Relativistic cosmology
83C45 Quantization of the gravitational field
83E05 Geometrodynamics and the holographic principle
81T20 Quantum field theory on curved space or space-time backgrounds
81T60 Supersymmetric field theories in quantum mechanics
53Z05 Applications of differential geometry to physics
85A40 Astrophysical cosmology