Symphony no.3 in E Flat; Hussite Overture

Anderson, Robert; Dvořák,; Lso,; Rowicki,

doi:10.2307/955782

Cited by 1 publication

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“…For Euclidean relational particle mechanics, these are P = N I=1 p I = 0 (zero total momentum for the model universe) and L = N I=1 q I × p I = 0 (zero total momentum for the model universe), while similarity relational particle mechanics has these again alongside D = N I=1 q I · p I = 0. By analogy with Example 3 below, relational particle mechanics are additionally useful models [31,32,33,34,27,17,18,35,36,37,38,28,24] for the Problem of Time in Quantum Gravity [32,39] and other issues of interest in Quantum Cosmology [40,41,42]. Example 2B) Relational particle mechanics can be cast in reduced form in spatial dimension 1 or 2.…”

Section: Examples Of Product-type Actionsmentioning

confidence: 99%

“…1) For models with 2-d configuration spaces such as for the minisuperspace models [52,56,57,58], quantum similarity relational particle mechanics of 3 particles in the plane [28,30] or of 4 particles on the line [29], and of 3 particles on the line with scale [36,23], the conformal value of ξ = {k − 2}/4{k − 1} collapses to zero, so that Laplacian ordering and conformally invariant wavefunctions suffice.…”

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confidence: 99%

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Relational motivation for conformal operator ordering in quantum cosmology

Anderson¹

2010

Class. Quantum Grav.

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Operator-ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering choice in quantum cosmology. It is particularly naturally and simply manifest in relationalist producttype actions (such as the Jacobi action for mechanics or Baierlein-Sharp-Wheeler type actions for general relativity), for which all that is required for the kinetic and potential factors to rescale in compensation to each other. These actions themselves mathematically sharply implementing philosophical principles relevant to whole-universe modelling, the motivation for conformal operator-ordering in quantum cosmology is substantially strengthened. Relationalist product-type actions also give emergent times which amount to recovering Newtonian, proper and cosmic time in the various relevant contexts. The conformal scaling of these actions directly tells us how emergent time scales; if one follows suit with the Newtonian time or the lapse in the more commonly used difference-type Euler-Lagrange or Arnowitt-Deser-Misner type actions, one sees how these too obey a more complicated conformal invariance. Moreover, our discovery of the conformal scaling of the time involved permits relating how it simplifies equations of motion with how affine parametrization simplifies geodesics.

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