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A special issue of Physics (ISSN 2624-8174). This special issue belongs to the section "High Energy Physics".

Deadline for manuscript submissions: closed (30 September 2022) | Viewed by 34596

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Prof. Dr. Shi-Dong Liang

E-Mail Website1 Website2
Guest Editor

School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
Interests: quantum physics; gravity theory; theoretical condensed matter physics

Prof. Dr. Tiberiu Harko

E-Mail Website
Guest Editor

1. Astronomical Observatory, 19 Ciresilor Street, 400487 Cluj-Napoca, Romania
2. Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Rumania
Interests: general relativity; cosmology; modified theories of gravity; dark matter and dark energy; Bose-Einstein Condensation; high energy astrophysics; stellar structure; mathematical physics; Jacobi stability; nonlinear dynamical systems
Special Issues, Collections and Topics in MDPI journals

Dr. Matthew J. Lake

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Guest Editor

1. National Astronomical Research Institute of Thailand, Chiang Mai 50180, Thailand
2. Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Interests: quantum gravity; quantum foundations; quantum information theory; high energy physics; astrophysics; cosmology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The expression ‘quantum geometry’ means many different things to many different people. Although virtually all researchers agree that the quantum theory of gravity, whatever form it may take, must involve a description of quantised spacetime, there is no accepted definition of this term. In this Special Issue, we invite contributions exploring the multi-faceted meanings of these two deceptively simple words.

We aim to collect together, in one volume, a range of works representing a broad overview of the diverse meanings attached to this innocent-sounding phrase over the past 95 years of research into quantum physics, information science, and gravity. Contibutions from all fields are welcome, without predudice or favour to any particular approach.

These include but are not necessarily limited to:

Noncommutative geometry;
Spin foams and loop quantum gravity;
Nonlocal geometry;
Generalised uncertainty relations and minimum length scenarios;
Quantum reference frames;
Emergent geometry from quantum entanglement and the ‘it from bit’ scenario;
Information geometry;
Stringy geometry;
Holographic geometry;
Causal dynamical triangulations, asymptotically safe gravity, and fractal spacetimes;
Weyl geometry in gravity and cosmology;
Finsler geometry in physics.

Works on other less mainstream approaches are also welcome and each article will be considered, independently, on its own merits. Papers may include original research or contain focussed reviews of different topics.

A comprehensive summary of such a huge field is, of course, impossible within a single volume, but we hope that this issue will provide a valuable reference, and starting point, for dialogue between diverse approaches to a common theme: the problem of quantum geometry.

Prof. Dr. Shi-Dong Liang
Prof. Dr. Tiberiu Harko
Dr. Matthew J. Lake
Guest Editors

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Physics is an international peer-reviewed open access quarterly journal published by MDPI.

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Keywords

noncommutative geometry
spin foams
nonlocal geometry
generalised uncertainty relations
quantum reference frames
quantum entanglement
information geometry
string geometry
holographic geometry
Weyl geometry
Finsler geometry

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Published Papers (14 papers)

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Editorial

Jump to: Research, Review

2 pages, 168 KiB

Open AccessEditorial

New Advances in Quantum Geometry

by Shi-Dong Liang, Tiberiu Harko and Matthew J. Lake

Physics 2023, 5(3), 688-689; https://doi.org/10.3390/physics5030045 - 30 Jun 2023

Cited by 1 | Viewed by 1597

Abstract

Presently, we are in a period of rapid and intensive changes in our understanding of the gravitational interaction, triggered by the important observational findings of the late 1990s [...] Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

Research

Jump to: Editorial, Review

26 pages, 396 KiB

Open AccessArticle

Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries

by Saulo Albuquerque, Valdir B. Bezerra, Iarley P. Lobo, Gabriel Macedo, Pedro H. Morais, Ernesto Rodrigues, Luis C. N. Santos and Gislaine Varão

Physics 2023, 5(1), 90-115; https://doi.org/10.3390/physics5010008 - 19 Jan 2023

Cited by 9 | Viewed by 1918

Abstract

In this paper, we reviewtwo approaches that can describe, in a geometrical way, the kinematics of particles that are affected by Planck-scale departures, named Finsler and Hamilton geometries. By relying on maps that connect the spaces of velocities and momenta, we discuss the properties of configuration and phase spaces induced by these two distinct geometries. In particular, we exemplify this approach by considering the so-called q-de Sitter-inspired modified dispersion relation as a laboratory for this study. We finalize with some points that we consider as positive and negative ones of each approach for the description of quantum configuration and phases spaces. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

10 pages, 427 KiB

Open AccessEditor’s ChoiceArticle

BFSS Matrix Model Cosmology: Progress and Challenges

by Suddhasattwa Brahma, Robert Brandenberger and Samuel Laliberte

Physics 2023, 5(1), 1-10; https://doi.org/10.3390/physics5010001 - 22 Dec 2022

Cited by 16 | Viewed by 2255

Abstract

We review a proposal to obtain an emergent metric space-time and an emergent early universe cosmology from the Banks–Fischler–Shenker–Susskind (BFSS) matrix model. Some challenges and directions for future research are outlined. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

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13 pages, 297 KiB

Open AccessArticle

On Momentum Operators Given by Killing Vectors Whose Integral Curves Are Geodesics

by Thomas Schürmann

Physics 2022, 4(4), 1440-1452; https://doi.org/10.3390/physics4040093 - 15 Dec 2022

Cited by 2 | Viewed by 1611

Abstract

The paper considers momentum operators on intrinsically curved manifolds. Given that momentum operators are Killing vector fields whose integral curves are geodesics, the corresponding manifold is flat or of the compact type with positive constant sectional curvature and dimensions equal to 1, 3, [...] Read more.

S^{3}

. It is verified that the structural constants of the underlying Lie algebra are proportional to 2

ℏ / R

, where R is the curvature radius of

S^{3}

and ℏ is the reduced Planck’s constant. This results in a countable energy and momentum spectrum of freely moving particles in

S^{3}

. The maximal resolution of the possible momenta is given by the de Broglie wave length,

λ_{R} = π R

, which is identical to the diameter of the manifold. The corresponding covariant position operators are defined in terms of geodesic normal coordinates, and the associated commutator relations of position and momentum are established. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

13 pages, 331 KiB

Open AccessArticle

On Majorization Uncertainty Relations in the Presence of a Minimal Length

by Alexey E. Rastegin

Physics 2022, 4(4), 1413-1425; https://doi.org/10.3390/physics4040091 - 14 Dec 2022

Cited by 1 | Viewed by 1470

Abstract

The emergence of a minimal length at the Planck scale is consistent with modern developments in quantum gravity. This is taken into account by transforming the Heisenberg uncertainty principle into the generalized uncertainty principle. Here, the position-momentum commutator is modified accordingly. In this paper, majorization uncertainty relations within the generalized uncertainty principle are considered. Dealing with observables with continuous spectra, each of the axes of interest is divided into a set of non-intersecting bins. Such formulation is consistent with real experiments with a necessarily limited precision. On the other hand, the majorization approach is mainly indicative for high-resolution measurements with sufficiently small bins. Indeed, the effects of the uncertainty principle are brightly manifested just in this case. The current study aims to reveal how the generalized uncertainty principle affects the leading terms of the majorization bound for position and momentum measurements. Interrelations with entropic formulations of this principle are briefly discussed. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

10 pages, 407 KiB

Open AccessArticle

Parametrization of Deceleration Parameter in f(Q) Gravity

by Gaurav N. Gadbail, Sanjay Mandal and Pradyumn Kumar Sahoo

Physics 2022, 4(4), 1403-1412; https://doi.org/10.3390/physics4040090 - 13 Dec 2022

Cited by 31 | Viewed by 2997

Abstract

In this paper, we investigate the modified symmetric teleparallel gravity or

f (Q)

gravity, where Q is the nonmetricity, to study the evolutionary history of the universe by considering the functional form of

f (Q) = α Q^{n}

[...] Read more.

In this paper, we investigate the modified symmetric teleparallel gravity or

f (Q)

gravity, where Q is the nonmetricity, to study the evolutionary history of the universe by considering the functional form of

f (Q) = α Q^{n}

, where

α

and n are constants. Here, we consider the parametrization form of the deceleration parameter as

q = q_{0} + q_{1} z / {(1 + z)}^{2}

(with the parameters

q_{0}

(q

z = 0)

q_{1}

, and the redshift, z), which provides the desired property for a sign flip from a decelerating to an accelerating phase. We obtain the solution of the Hubble parameter by examining the mentioned parametric form of q, and then we impose the solution in Friedmann equations. Employing the Bayesian analysis for the Observational Hubble data (OHD), we estimated the constraints on the associated free parameters

(H_{0}, q_{0}, q_{1})

with

H_{0}

the current Hubble parameter to determine if this model may challenge the

Λ

CDM (

Λ

cold dark matter with the cosmological constant,

Λ

) limitations. Furthermore, the constrained current value of the deceleration parameter

q_{0} = - 0 . 832_{- 0.091}^{+ 0.091}

shows that the present universe is accelerating. We also investigate the evolutionary trajectory of the energy density, pressure, and EoS (equation-of-state) parameters to conclude the accelerating behavior of the universe. Finally, we try to demonstrate that the considered parametric form of the deceleration parameter is compatible with

f (Q)

gravity. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

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19 pages, 340 KiB

Open AccessArticle

Exploring Quantum Geometry Created by Quantum Matter

by Abhay Ashtekar

Physics 2022, 4(4), 1384-1402; https://doi.org/10.3390/physics4040089 - 8 Dec 2022

Cited by 1 | Viewed by 1617

Abstract

Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized. The goal of this investigation is to probe the ‘Coulombic’ aspects of quantum geometry that are governed entirely by matter sources. Since there are no gravitational waves in three dimensions, 3-dimensional (3-d) gravity coupled to matter provides an ideal arena for this task. The analysis presented here reveals novel aspects of quantum gravity that bring out limitations of classical and semi-classical theories in unforeseen regimes: non-linearities of general relativity can magnify small quantum fluctuations in the matter sector to large effects in the gravitational sector. Finally, this analysis leads to thought experiments that bring out rather starkly why understanding of the nature of physical reality depends sensitively on the theoretical lens with which it is probed. As theories become richer, new scales emerge, triggering novel effects that could not be imagined before. The model provides a concise realization of this well-known chain. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

11 pages, 359 KiB

Open AccessArticle

The Cosmology of a Non-Minimally Coupled f(R,T) Gravitation

by Değer Sofuoğlu, Rishi Kumar Tiwari, Amare Abebe, Alnadhief H. A. Alfedeel and Eltegani I. Hassan

Physics 2022, 4(4), 1348-1358; https://doi.org/10.3390/physics4040086 - 7 Nov 2022

Cited by 11 | Viewed by 1645

Abstract

A non-minimally coupled cosmological scenario is considered in the context of

f (R, T) = f_{1} (R) + f_{2} (R) f_{3} (T)

gravity (with R being the Ricci scalar and T [...] Read more.

A non-minimally coupled cosmological scenario is considered in the context of

f (R, T) = f_{1} (R) + f_{2} (R) f_{3} (T)

gravity (with R being the Ricci scalar and T the trace of the energy-momentum tensor) in the background of the flat Friedmann–Robertson–Walker (FRW) model. The field equations of this modified theory are solved using a time-dependent deceleration parameter for a dust. The behavior of the model is analyzed taking into account constraints from recent observed values the deceleration parameter. It is shown that the analyzed models can explain the transition from the decelerating phase to the accelerating one in the expansion of the universe, by staying true to the results of the observable universe. It is shown that the models are dominated by a quintessence-like cosmological dark fluid at the late universe. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

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13 pages, 509 KiB

Open AccessArticle

Generalized Extended Uncertainty Principle Black Holes: Shadow and Lensing in the Macro- and Microscopic Realms

by Nikko John Leo S. Lobos and Reggie C. Pantig

Physics 2022, 4(4), 1318-1330; https://doi.org/10.3390/physics4040084 - 28 Oct 2022

Cited by 26 | Viewed by 2747

Abstract

Motivated by the recent study about the extended uncertainty principle (EUP) black holes, we present in this study its extension called the generalized extended uncertainty principle (GEUP) black holes. In particular, we investigated the GEUP effects on astrophysical and quantum black holes. First, we derive the expression for the shadow radius to investigate its behavior as perceived by a static observer located near and far from the black hole. Constraints to the large fundamental length scale,

L_{*}

, up to two standard deviations level were also found using the Event Horizont Telescope (EHT) data: for black hole Sgr. A*,

L_{*} = 5.716 \times 10^{10}

m, while for M87* black hole,

L_{*} = 3.264 \times 10^{13}

m. Under the GEUP effect, the value of the shadow radius behaves the same way as in the Schwarzschild case due to a static observer, and the effect only emerges if the mass, M, of the black hole is around the order of magnitude of

L_{*}

(or the Planck length,

l_{Pl}

). In addition, the GEUP effect increases the shadow radius for astrophysical black holes, but the reverse happens for quantum black holes. We also explored GEUP effects to the weak and strong deflection angles as an alternative analysis. For both realms, a time-like particle gives a higher value for the weak deflection angle. Similar to the shadow, the deviation is seen when the values of

L_{*}

and M are close. The strong deflection angle gives more sensitivity to GEUP deviation at smaller masses in the astrophysical scenario. However, the weak deflection angle is a better probe in the micro world. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

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12 pages, 299 KiB

Open AccessArticle

Cosmology of a Polynomial Model for de Sitter Gauge Theory Sourced by a Fluid

by Jia-An Lu

Physics 2022, 4(4), 1168-1179; https://doi.org/10.3390/physics4040076 - 2 Oct 2022

Cited by 1 | Viewed by 1473

Abstract

In the de Sitter gauge theory (DGT), the fundamental variables are the de Sitter (dS) connection and the gravitational Higgs/Goldstone field

ξ^{A}

, where A is a 5 dimensional index. Previously, a model for DGT was analyzed, which generalizes the MacDowell–Mansouri gravity [...] Read more.

In the de Sitter gauge theory (DGT), the fundamental variables are the de Sitter (dS) connection and the gravitational Higgs/Goldstone field

ξ^{A}

, where A is a 5 dimensional index. Previously, a model for DGT was analyzed, which generalizes the MacDowell–Mansouri gravity to have a variable cosmological constant,

Λ = 3 / l^{2}

, where l is related to

ξ^{A}

ξ^{A} ξ_{A} = l^{2}

. It was shown that the model sourced by a perfect fluid does not support a radiation epoch and the accelerated expansion of the parity invariant universe. In this paper, I consider a similar model, namely, the Stelle–West gravity, and couple it to a modified perfect fluid, such that the total Lagrangian 4-form is polynomial in the gravitational variables. The Lagrangian of the modified fluid has a nontrivial variational derivative with respect to l, and as a result, the problems encountered in the previous study no longer appear. Moreover, to explore the elegance of the general theory, as well as to write down the basic framework, I perform the Lagrange–Noether analysis for DGT sourced by a matter field, yielding the field equations and the identities with respect to the symmetries of the system. The resulted formula are dS covariant and do not rely on the existence of the metric field. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

22 pages, 1375 KiB

Open AccessArticle

Why Do Elementary Particles Have Such Strange Mass Ratios?—The Importance of Quantum Gravity at Low Energies

by Tejinder P. Singh

Physics 2022, 4(3), 948-969; https://doi.org/10.3390/physics4030063 - 25 Aug 2022

Cited by 8 | Viewed by 3542

Abstract

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infra-red. Using the octonions as space-time coordinates, we construct pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries [...] Read more.

S U {(2)}_{R}

chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

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26 pages, 557 KiB

Open AccessArticle

Effects of Quantum Metric Fluctuations on the Cosmological Evolution in Friedmann-Lemaitre-Robertson-Walker Geometries

by Zahra Haghani and Tiberiu Harko

Physics 2021, 3(3), 689-714; https://doi.org/10.3390/physics3030042 - 24 Aug 2021

Cited by 7 | Viewed by 3122

Abstract

In this paper, the effects of the quantum metric fluctuations on the background cosmological dynamics of the universe are considered. To describe the quantum effects, the metric is assumed to be given by the sum of a classical component and a fluctuating component of quantum origin . At the classical level, the Einstein gravitational field equations are equivalent to a modified gravity theory, containing a non-minimal coupling between matter and geometry. The gravitational dynamics is determined by the expectation value of the fluctuating quantum correction term, which can be expressed in terms of an arbitrary tensor

K_{μ ν}

. To fix the functional form of the fluctuation tensor, the Newtonian limit of the theory is considered, from which the generalized Poisson equation is derived. The compatibility of the Newtonian limit with the Solar System tests allows us to fix the form of

K_{μ ν}

. Using these observationally consistent forms of

K_{μ ν}

, the generalized Friedmann equations are obtained in the presence of quantum fluctuations of the metric for the case of a flat homogeneous and isotropic geometry. The corresponding cosmological models are analyzed using both analytical and numerical method. One finds that a large variety of cosmological models can be formulated. Depending on the numerical values of the model parameters, both accelerating and decelerating behaviors can be obtained. The obtained results are compared with the standard

Λ

CDM (

Λ

Cold Dark Matter) model. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

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Review

Jump to: Editorial, Research

25 pages, 397 KiB

Open AccessReview

An Introduction to Noncommutative Physics

by Shi-Dong Liang and Matthew J. Lake

Physics 2023, 5(2), 436-460; https://doi.org/10.3390/physics5020031 - 18 Apr 2023

Cited by 7 | Viewed by 3099

Abstract

Noncommutativity in physics has a long history, tracing back to classical mechanics. In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics in a range of areas, including classical physics, condensed matter systems, statistical mechanics, and quantum mechanics, and we present some important examples of noncommutative algebras, including the classical Poisson brackets, the Heisenberg algebra, Lie and Clifford algebras, the Dirac algebra, and the Snyder and Nambu algebras. Potential applications of noncommutative structures in high-energy physics and gravitational theory are also discussed. In particular, we review the formalism of noncommutative quantum mechanics based on the Seiberg–Witten map and propose a parameterization scheme to associate the noncommutative parameters with the Planck length and the cosmological constant. We show that noncommutativity gives rise to an effective gauge field, in the Schrödinger and Pauli equations. This term breaks translation and rotational symmetries in the noncommutative phase space, generating intrinsic quantum fluctuations of the velocity and acceleration, even for free particles. This review is intended as an introduction to noncommutative phenomenology for physicists, as well as a basic introduction to the mathematical formalisms underlying these effects. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

23 pages, 458 KiB

Open AccessReview

The Barbero–Immirzi Parameter: An Enigmatic Parameter of Loop Quantum Gravity

by Rakshit P. Vyas and Mihir J. Joshi

Physics 2022, 4(4), 1094-1116; https://doi.org/10.3390/physics4040072 - 20 Sep 2022

Cited by 3 | Viewed by 2363

Abstract

The Barbero–Immirzi parameter, (γ), is introduced in loop quantum gravity (LQG), whose physical significance is still the biggest open question because of its profound traits. In some cases, it is real valued, while it is complex valued in other cases. This parameter emerges in the process of denoting a Lorentz connection with a non-compact group SO(3,1) in the form of a complex connection with values in a compact group of rotations, either SO(3) or SU(2). Initially, it appeared in the Ashtekar variables. Fernando Barbero proposed its possibility for inclusion within formalism. Its present value is fixed by counting micro states in loop quantum gravity and matching with the semi-classical black hole entropy computed by Stephen Hawking. This parameter is used to count the size of the quantum of area in Planck units. Until the discovery of the spectrum of the area operator in LQG, its significance remained unknown. However, its complete physical significance is yet to be explored. In the present paper, an introduction to the Barbero–Immirzi parameter in LQG, a timeline of this research area, and various proposals regarding its physical significance are given. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

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