caa a22 4500 445387432 CHVBK 20180317143036.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s10714-010-1140-z doi (NATIONALLICENCE)springer-10.1007/s10714-010-1140-z Anderson Edward DAMTP, Cambridge, UK aut Shape space methods for quantum cosmological triangleland [Elektronische Daten] [Edward Anderson] With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so by importing techniques to the triangle model from the corresponding 4 particles in 1-d model, using the fact that both have 2-spheres for shape spaces, though the latter has a trivial realization whilst the former has a more involved Hopf (or Dragt) type realization. I furthermore interpret the ensuing Dragt-type coordinates as shape quantities: a measure of anisoscelesness, the ellipticity of the base and apex's moments of inertia, and a quantity proportional to the area of the triangle. I promote these quantities at the quantum level to operators whose expectation and spread are then useful in understanding the quantum states of the system. Additionally, I tessellate the 2-sphere by its physical interpretation as the shape space of triangles, and then use this as a back-cloth from which to read off the interpretation of dynamical trajectories, potentials and wavefunctions. I include applications to timeless approaches to the problem of time and to the role of uniform states in quantum cosmological modelling. Springer Science+Business Media, LLC, 2011 Relational particle mechanics nationallicence Toy models of geometrodynamics nationallicence Problem of time nationallicence Quantum cosmology nationallicence General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/5(2011-05-01), 1529-1548 0001-7701 43:5<1529 2011 43 10714 https://doi.org/10.1007/s10714-010-1140-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-010-1140-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Anderson Edward DAMTP, Cambridge, UK aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/5(2011-05-01), 1529-1548 0001-7701 43:5<1529 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer