Faithful realizations of semiclassical truncations

Baytaş, Bekir; Bojowald, Martin; Crowe, Sean

doi:10.1016/j.aop.2020.168247

Cited by 21 publications

(26 citation statements)

References 45 publications

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“…where λ s are time dependent coefficients and |e i are basis vectors. The Legendre transformation yields q → δS δ q = p, λi → δS δ λi = iλ * i , (41) and the canonical structure is given by the symplectic form…”

Section: Discussionmentioning

confidence: 99%

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Quantum dynamics in Weyl-Heisenberg coherent states

Miroszewski¹

2020

Preprint

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The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems into 'classical' and 'quantum' degrees of freedom. The decomposition is found to be equivalent to quantum mechanics perceived from a semi-classical frame. The split allows for introduction of a new definition of classical state and is a convenient starting point for approximate analysis of quantum dynamics. An example of a meta-stable state is given as a practical illustration of the introduced concepts.

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Section: Discussionmentioning

confidence: 99%

“…Another possible extension of the lower symbol method is the moments expansion. The method is well known for years and becomes reinvented every once in a while in context of different fields [38][39][40][41]. It introduces the notion of moments of the wave function.…”

Section: Moments Expansion Methodsmentioning

confidence: 99%

Quantum dynamics in Weyl-Heisenberg coherent states

Miroszewski¹

2020

Preprint

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“…It is possible to extend this canonical effective formulation to higher orders of moments [26]. Results obtained up to fourth order [27] suggest the generic behavior ∆(Q 2n ) ∼ s 2n and ∆(Q 2n+1 ) = 0 for a suitable class of states.…”

Section: The Spherical Minisuperspace Model: Canonical Effective Methodsmentioning

confidence: 96%

“…If there is a non-zero third-order moment, there would be an additional contribution proportional to the third derivative of Q 3/2 (1−x) . Assuming that a third-order moment of Q is proportional to s 3 (as suggested by [26,27]), this new term could be of the form V −3/2 provided the third derivative of Q 3/2(1−x) has the same form as the second derivative of…”

Section: Non-gaussianitymentioning

confidence: 99%

Minisuperspace results for causal dynamical triangulations

Baytaş

Bojowald

Crowe

et al. 2020

J. Cosmol. Astropart. Phys.

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Detailed applications of minisuperspace methods are presented and compared with results obtained in recent years by means of causal dynamical triangulations (CDTs), mainly in the form of effective actions. The analysis sheds light on conceptual questions such as the treatment of time or the role and scaling behavior of statistical and quantum fluctuations. In the case of fluctuations, several analytical and numerical results show agreement between the two approaches and offer possible explanations of effects that have been seen in causal dynamical triangulations but whose origin remained unclear. The new approach followed here suggests "CDT experiments" in the form of new simulations or evaluations motivated by theoretical predictions, testing CDTs as well as the minisuperspace approximation.

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“…Independent fields for quantum corrections have been used in similar models analyzed in [3][4][5][6]. The relationship between these fields and moments of an evolving state follows from the canonical effective theory of [7,8], written in terms of Casimir-Darboux variables that bring the phase-space structure of moments to canonical form [9,10]. In general, deriving Casimir-Darboux variables that coordinatize phase space by pairs of position and momentum coordinates as well as conserved quantities (the Casimir variables) is a challenging task in higherdimensional cases as presented by moment systems in particular in a case of field theory.…”

Section: Introductionmentioning

confidence: 99%

Quasiclassical model of inhomogeneous cosmology

Bojowald

Freddy

2023

Class. Quantum Grav.

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Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of eﬀective potentials. In addition, space-time properties are relevant in cosmology, in particular when combined with quantum corrections required to maintain general covariance in a consistent way. Here, an extension of previous investigations of static quasiclassical space-time models to dynamical ones is presented, describing the evolution of 1-dimensional space as in the classical Lemaitre–Tolman–Bondi models. The corresponding spatial metric has two independent components, both of which are in general subject to quantum ﬂuctuations. The main result is that individual moments from both components are indeed required for general covariance to be maintained at a semiclassical level, while quantum correlations between the components are less relevant.

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Faithful realizations of semiclassical truncations

Cited by 21 publications

References 45 publications

Quantum dynamics in Weyl-Heisenberg coherent states

Quantum dynamics in Weyl-Heisenberg coherent states

Minisuperspace results for causal dynamical triangulations

Quasiclassical model of inhomogeneous cosmology

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