Relational Motivation for Conformal Operator Ordering in Quantum Cosmology - General Relativity and Quantum CosmologyReportar como inadecuado




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Abstract: Operator-ordering in quantum cosmology is a major as-yet unsettled ambiguitywith not only formal but also physical consequences. We determine theLagrangian origin of the conformal invariance that underlies the conformaloperator-ordering choice in quantum cosmology. It is particularly naturally andsimply manifest in relationalist product-type actions such as the Jacobiaction for mechanics or Baierlein-Sharp-Wheeler type actions for generalrelativity, for which all that is required for the kinetic and potentialfactors to rescale in compensation to each other. These actions themselvesmathematically sharply implementing philosophical principles relevant towhole-universe modelling, the motivation for conformal operator-ordering inquantum cosmology is substantially strengthened. Relationalist product-typeactions also give emergent times which amount to recovering Newtonian, properand cosmic time in the various relevant contexts. The conformal scaling ofthese actions directly tells us how emergent time scales; if one follows suitwith the Newtonian time or the lapse in the more commonly used difference-typeEuler-Lagrange or Arnowitt-Deser-Misner type actions, one sees how these tooobey a more complicated conformal invariance. Moreover, our discovery of theconformal scaling of the time involved permits relating how it simplifiesequations of motion with how affine parametrization simplifies geodesics.



Autor: Edward Anderson

Fuente: https://arxiv.org/







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