A new bound on polymer quantization via an opto-mechanical setup

Khodadi, Mohsen; Dey, Sanjib; Bhat, Abdul Hamid; Faizal, Mir

doi:10.1038/s41598-018-19181-9

Cited by 45 publications

(34 citation statements)

References 56 publications

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“…where we have considered the condition p u = 0. This expression results exactly the uncertainty relation obtained by [32], which is completely analogous to the ones appearing within the context of generalized uncertainty principle (GUP) scenarios analyzed within String Theory and Loop Quantum Gravity [16], [31], [33]. Nevertheless, in the case of the polymer representation there is a key difference with respect to the GUP's.…”

Section: The Uncertainty Principlesupporting

confidence: 80%

Polymer quantum mechanics as a deformation quantization

Berra─Montiel

Molgado

2018

Class. Quantum Grav.

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We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer representation as a distributional limit of the Schrödinger representation for the Weyl algebra in a Gaussian weighted measure, and we observe that the quasi-probability distribution limit of this Schrödinger representation agrees with the Wigner function for Loop Quantum Cosmology. Further, the introduced polymer star-product fulfills Bohr's correspondence principle even though not all the operators are well defined in the polymer representation. Finally, within our framework, we also derive a generalized uncertainty principle which resembles the one appearing in different scenarios, including theories with a minimal length.

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Section: The Uncertainty Principlesupporting

confidence: 80%

Polymer quantum mechanics as a deformation quantization

Berra─Montiel

Molgado

2018

Class. Quantum Grav.

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“…However, many studies have appeared in literature, with the aim to set bounds on (see, for instance, Refs. [ 20 – 24 ]).…”

Section: Introductionmentioning

confidence: 99%

Modified Unruh effect from generalized uncertainty principle

et al. 2018

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We consider a generalized uncertainty principle (GUP) corresponding to a deformation of the fundamental commutator obtained by adding a term quadratic in the momentum. From this GUP, we compute corrections to the Unruh effect and related Unruh temperature, by first following a heuristic derivation, and then a more standard field theoretic calculation. In the limit of small deformations, we recover the thermal character of the Unruh radiation. Corrections to the temperature at first order in the deforming parameter are compared for the two approaches, and found to be in agreement as for the dependence on the cubic power of the acceleration of the reference frame. The dependence of the shifted temperature on the frequency is also pointed out and discussed.

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“…However, we do not identify a mechanism for the reduction of the Cosmological Constant value to the actual one. A qualitative implementation of the upper limits for a Polymer cut-off on the physical space [20] provides a vacuum energy density many orders of magnitude greater than the one requested by the Universe acceleration. We can only stress that the calculated ground state of the scalar field Hamiltonian function is not a state for the quantum dynamics of the system and, therefore, we dynamically have to deal with a time dependent expectation value on the vacuum state of the scalar field.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical and quantum polymer effects in a flat isotropic universe

et al. 2019

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We analyze some relevant semiclassical and quantum features of the implementation of Polymer Quantum Mechanics to the phenomenology of the flat isotropic Universe.We firstly investigate a parallelism between the semiclassical polymer dynamics of the flat isotropic Universe, as reduced to the effect of a modified simplectic structure, and the so-called Generalized Uncertainty Principle. We show how the difference in the sign of the fundamental Poisson bracket is reflected in a sign of the modified source term in the Friedmann equation, responsible for the removal of the initial singularity in the polymer case and for the survival of a singular point in the Universe past, when the Generalized Uncertainty Principle is concerned.Then, we study the regularization of the vacuum energy of a free massless scalar field, by implementing a second quantization formalism in the context of Polymer Quantum Mechanics. We show that, from this reformulation, naturally emerges a Cosmological Constant term for the isotropic Universe, whose value depends directly on the polymer parameter of the regularization.Finally, we investigate the behaviour of gravitational waves on the background of a modified dynamics, according to the semiclassical Friedmann equation. We demonstrate that the presence of a Bounce in the Universe past, naturally removes the divergence of the gravitational wave amplitude and they can, in principle, propagate across the minimum volume turning point. This result offers the intriguing perspective for the detection of gravitational signals coming from the pre-Big Bounce collapsing Universe.

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A new bound on polymer quantization via an opto-mechanical setup

Cited by 45 publications

References 56 publications

Polymer quantum mechanics as a deformation quantization

Polymer quantum mechanics as a deformation quantization

Modified Unruh effect from generalized uncertainty principle

Semiclassical and quantum polymer effects in a flat isotropic universe

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