Relational motivation for conformal operator ordering in quantum cosmology

Anderson, Edward

doi:10.1088/0264-9381/27/4/045002

Cited by 13 publications

(38 citation statements)

References 76 publications

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“…also of the form in eq (24)]. In fact, the two are related by a conformal transformation, which is a relationallymotivated freedom [63]. Thus they lie within the same theoretical scheme from the Machian perspective.…”

Section: Recasting Of the L-fluctuation Equation As A Tdsementioning

confidence: 97%

Machian classical and semiclassical emergent time

Anderson¹

2013

Class. Quantum Grav.

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Classical and semiclassical schemes are presented that are timeless at the primary level and recover time from Mach's 'time is to be abstracted from change' principle at the emergent secondary level. The semiclassical scheme is a Machian variant of the Semiclassical Approach to the Problem of Time in Quantum Gravity. The classical scheme is Barbour's, cast here explicitly as the classical precursor of the Semiclassical Approach. Thus the two schemes have been married up, as equally-Machian and necessarily distinct, since the latter's timestandard is abstracted in part from quantum change. I provide perturbative schemes for these in which the timefunction is to be determined rather than assumed. This paper is useful modelling as regards the Halliwell-Hawking arena for the quantum origin of the inhomogeneous cosmological fluctuations.

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Section: Recasting Of the L-fluctuation Equation As A Tdsementioning

confidence: 97%

Machian classical and semiclassical emergent time

Anderson¹

2013

Class. Quantum Grav.

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“…while elements of the self-adjoint extension ofH corresponding to the angle θ in Span{ϕ (1) , ϕ (2) } behave asymptotically as (5.15) near y = 0. For |J + | < 1 2 , the condition (6.1) can only be satisfied when C = 0, meaning that D(T β ) ∩ D(Ṽ ) satisfies the boundary conditions of all selfadjoint extensions ofH, and thusH is not essentially self-adjoint on D(T β ) ∩ D(Ṽ ).…”

Section: Formulation Of the Propagator And Path-integral Representatimentioning

confidence: 99%

“…Since ϕ (1) ∼ C 1 y −|J + |+ 1 2 , ϕ (2) ∼ C 2 y |J + |+ 1 2 , (6.4) can only be satisfied if θ = 0, identifying T β+Ṽ as the self-adjoint extension ofH purely in Span{ϕ (2) } (for all β).…”

Section: Formulation Of the Propagator And Path-integral Representatimentioning

confidence: 99%

Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions

Haga¹,

Maitra²

2017

SIGMA

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Abstract. We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the time-evolution operator, one requires that the corresponding Hamiltonian is self-adjoint; this issue is subtle for a particular category of factor orderings. We identify and parametrize a complete set of self-adjoint extensions and provide a canonical description of these extensions in terms of boundary conditions. Moreover, we use Trotter-type product formulae to construct path-integral representations of time evolution.

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“…The above uses the conformal ordering; for 2 − d configuration spaces as in the present paper, this furthermore coincides with the sometimes also-advocated Laplacian ordering. (See [23] and references therein for arguments for these operator orderings in quantum cosmological modelling. )…”

Section: Quantum Trianglelandmentioning

confidence: 99%

“…Such characteristics motivate RPM's as whole-universe models for the Problem of Time in Quantum Gravity [26,[31][32][33][36][37][38][39][40], for other foundational issues in Quantum Cosmology [15,[40][41][42] and as examples of quantization procedures. As well as the opening sentence's references, see also [7,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] for RPM's used in these ways.…”

Section: Introductionmentioning

confidence: 99%

Shape space methods for quantum cosmological triangleland

Anderson

2011

Gen Relativ Gravit

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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 backcloth 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.

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Relational motivation for conformal operator ordering in quantum cosmology

Cited by 13 publications

References 76 publications

Machian classical and semiclassical emergent time

Machian classical and semiclassical emergent time

Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions

Shape space methods for quantum cosmological triangleland

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