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- W2057931434 abstract "We provide the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are ℂℙ 2 and the cone over this. We consider exact free and isotropic HO potential cases and perturbations about these. Moreover, our purely relational kinematical quantization is distinct from the usual one for ℂℙ 2 , which turns out to carry absolutist connotations instead. Thus, this paper is the first to note absolute-versus-relational motion distinctions at the kinematical rather than dynamical level. It is also an example of value to the discussion of kinematical quantization along the lines of Isham, 1984. The relational quadrilateral is the simplest RPM whose mathematics is not standard in atomic physics (the triangle and four particles on a line are both based on 𝕊 2 and ℝ 3 mathematics). It is far more typical of the general quantum relational N-a-gon than the previously studied case of the relational triangle. We consider useful integrals as regards perturbation theory and the peaking interpretation of quantum cosmology. We subsequently consider problem of time (PoT) applications of this: quantum Kuchař beables, the Machian version of the semiclassical approach and the timeless naïve Schrödinger interpretation. These go toward extending the combined Machian semiclassical-Histories-Timeless Approach of [Int. J. Mod. Phys. D23 (2014) 1450014] to the case of the quadrilateral, which will be treated in subsequent papers." @default.
- W2057931434 created "2016-06-24" @default.
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- W2057931434 date "2014-04-30" @default.
- W2057931434 modified "2023-10-10" @default.
- W2057931434 title "Relational quadrilateralland II: The Quantum Theory" @default.
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- W2057931434 doi "https://doi.org/10.1142/s0218271814500527" @default.
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