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- W2788763023 abstract "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 scalefree triangle formed by 3 particles in 2-d. The shape spaces (configuration spaces for scalefree systems) both for this and for 4 particles in 1-d are spheres. Three quantities u whose squares sum to one play the role of Cartesian coordinates for an auxiliary surrounding flat 3-space and are then good variables from the perspective of kinematical quantization. These quantities turn out to be obvious ratios of relative separations for 4 particles in 1-d and rather less trivial Dragt-type coordinates in the case of the triangle. In each case, the u furthermore admit useful interpretation as shape quantities; the triangle's three Dragt-type coordinates are an ellipicity of the system's moments of inertia, a measure of anisoscelesness and the triangle's area up to proportionality. 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 mass-weighted shape sphere by its physical interpretation as the triangle, which parallels partitioning the night sky zodiacally and austro-boreally; juxtaposing this with classical trajectories/quantum mechanical wavefunctions permits straightforward reading off of the sequence of triangles in the motion/how probable each triangle is. I explain how features desirable for quantum cosmology cause one's models to depart in detail from somewhat similar models already studied in molecular physics. I include applications to multiverse modelling and to timeless approaches to the problem of time." @default.
- W2788763023 created "2018-03-06" @default.
- W2788763023 creator A5035254527 @default.
- W2788763023 date "2009-09-13" @default.
- W2788763023 modified "2023-09-27" @default.
- W2788763023 title "Shape Operators and Zodiac Tessellation: Improved Interpretation of Quantum Cosmological Triangleland" @default.
- W2788763023 hasPublicationYear "2009" @default.
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