Exact classical correspondence in quantum cosmology

John, Moncy V.

doi:10.1134/s0202289315030044

Cited by 8 publications

(5 citation statements)

References 23 publications

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“…Furthermore, the Hamiltonian expectation values -physically the volume of the universe up to a constant, analogous to the notion of energy in quantum mechanics of more conventional systems -also match the evolution of the classical volume (this is true without the provisos). A similar quantum-classical correspondence was established using de Broglie-Bohm theory for other appropriate matter content with standard cosmological time and outside the reduced-Hamiltonian picture in [65]. While such results are encouraging, the equality of classical and quantum trajectories is not necessary for the method described here to be applied.…”

Section: Canonical Quantisation Of York-time Cosmological Perturbatio...supporting

confidence: 52%

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Gravitation and cosmology with York time

Roser¹

2016

Preprint

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Despite decades of inquiry an adequate theory of 'quantum gravity' has remained elusive, in part due to the absence of data that would guide the search and in part due to technical difficulties, prominently among them the 'problem of time'. The problem is a result of the attempt to quantise a classical theory with temporal reparameterisation and refoliation invariance such as general relativity.One way forward is therefore the breaking of this invariance via the identification of a preferred foliation of spacetime into parameterised spatial slices. In this thesis we argue that a foliation into slices of constant extrinsic curvature, parameterised by 'York time', is a viable contender. We argue that the role of York time in the initial-value problem of general relativity as well as a number of the parameter's other properties make it the most promising candidate for a physically preferred notion of time.A Hamiltonian theory describing gravity in the York-time picture may be derived from general relativity by 'Hamiltonian reduction', a procedure that eliminates certain degrees of freedom -specifically the local scale and its rate of change -in favour of an explicit time parameter and a functional expression for the associated Hamiltonian. In full generality this procedure is impossible to carry out since the equation that determines the Hamiltonian cannot be solved using known methods.However, it is possible to derive explicit Hamiltonian functions for cosmological scenarios (where matter and geometry is treated as spatially homogeneous). Using a perturbative expansion of the unsolvable equation enables us to derive a quantisable Hamiltonian for cosmological perturbations on such a homogeneous background. We analyse the (classical) theories derived in this manner and look at the York-time description of a number of cosmological processes.We then proceed to apply the canonical quantisation procedure to these systems and analyse the resulting quantum theories. We discuss a number of conceptual and technical points, such as the notion of volume eigenfunctions and the absence of a momentum representation as a result of the non-canonical commutator structure. While not problematic in a technical sense, the conceptual problems with canonical quantisation are particularly apparent when the procedure is applied in cosmological contexts.In the final part of this thesis we develop a new quantisation method based on configuration-space trajectories and a dynamical configuration-space Weyl geometry. There is no wavefunction in this type of quantum theory and so many of the conceptual issues do not arise. We outline the application of this quantisation procedure to gravity and discuss ter Institute during 2012/2013, where a non-trivial amount of the research in this thesis (especially chapter 11) was carried out. I furthermore wish to thank Lee Smolin, who in early 2012 pointed me toward the literature on the then very recent developments in Shape Dynamics, and Rafael Sorkin, whose critical and novel way to look at questions in...

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Section: Canonical Quantisation Of York-time Cosmological Perturbatio...supporting

confidence: 52%

“…Fortunately, the results obtained with the present method are however encouraging. The pseudo-classical behaviour of the quantum trajectories (see below) has also been deduced by John[65], although without reference to York time and with a slightly expanded notion of quantum trajectory.…”

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confidence: 99%

Gravitation and cosmology with York time

Roser¹

2016

Preprint

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“…An alternative approach is to obtain the quantum trajectories of the given wave function and to check whether these trajectories agree with the classical ones, at least in the limiting case. We have seen in [12] that the coasting evolution of the universe that starts from a singularity will have exact classical-quantum correspondence when checked in this manner. We show, using the MdBB complex trajectory formulation of quantum mechanics, that in the present case of complex cosmology too, there is exact correspondence between the quantum and classical description of the universe, throughout its history of evolution.…”

Section: Classical-quantum Correspondencementioning

confidence: 96%

“…This was only partially successful, for we could get only an approximate solution that describes the late classical epoch of the universe. In [12], using the 'quantum trajectories' approach, we checked whether the coasting evolution of a universe that starts from singularity [4] will have exact quantum-classical correspondence and obtained a positive result. In that case, we have used the de Broglie-Bohm (dBB) [13,14] and modified de Broglie-Bohm (MdBB) [15][16][17][18][19][20] trajectory formulations of quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Bouncing and Coasting Universe with Exact Quantum-Classical Correspondence

John¹

2021

Int J Theor Phys

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When the scale factor of expansion of the universe is written as a(t) ≡ Ae α (t) , with A as some real constant and α(t) a real function, the gravitational action I G appears in the same form as the matter action I M for a homogeneous and isotropic scalar field with a specific scale factor-dependent potential. We observe that by making analytic continuation of the Lagrangian function in this I G to the complex plane of α, one can obtain terms corresponding to both parts of a total action that describes a viable cosmological model. The solution gives a bouncing and coasting universe, which first contracts and then expands linearly, with a smooth bounce in between them. Such a bounce, called a Tolman wormhole, is due to a Casimir-like negative energy that appears naturally in the solution. In a novel approach to quantum cosmology, we perform canonical quantization of the above model using the operator method and show that it can circumvent the operator ordering ambiguity in the conventional formalism. It leads to a quantum wave equation for the universe, solving which we get the interesting result that the universe is in a ground state with nonzero energy. This solution is different from the Wheeler-DeWitt wave function and possesses exact quantum-classical correspondence during all epochs.

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“…In particular, it may be worth investigating quan-tum properties and their correspondence with classical properties for the inverted oscillator, which can be applied in the description of fundamental inflation models in cosmology [9,10], black hole physics with and without Rindler observers [11][12][13][14][15][16], string theory [17,18], the Wheeler-DeWitt minisuperspace problem [19,20], etc. The quantum-classical correspondence in the development of cosmologies is important in order to meet the condition that a given cosmological model is robust [21][22][23][24][25]. Quantum descriptions of the inverted oscillator are somewhat unfamiliar and mathematical handling of such a system is not so easy, even if its classical analysis is relatively well known.…”

Section: Introductionmentioning

confidence: 99%

Quantum-classical correspondence for the inverted oscillator

Maamache

Choi

2017

Chinese Phys. C

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While quantum-classical correspondence for a system is a very fundamental problem in modern physics, the understanding of its mechanism is often elusive, so the methods used and the results of detailed theoretical analysis have been accompanied by active debate. In this study, the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution. The inverted oscillator model plays an important role in several branches of cosmology and particle physics. The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them. It is shown from illustrations of the probability density that, although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one, the difference becomes relatively small when the classical excitation is sufficiently high. We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave. From these main interpretations and others in the text, we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system, which is a crucial concept in quantum mechanics.

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Exact classical correspondence in quantum cosmology

Cited by 8 publications

References 23 publications

Gravitation and cosmology with York time

Gravitation and cosmology with York time

Bouncing and Coasting Universe with Exact Quantum-Classical Correspondence

Quantum-classical correspondence for the inverted oscillator

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