6. Frontiers of gravitational physics

2017 ◽  
pp. 83-97
Author(s):  
Timothy Clifton
Keyword(s):  
Quantum Mechanics ◽  
String Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Loop Quantum Gravity ◽  
Gravitational Interaction ◽  
Theoretical Description ◽  
Theoretical Physics ◽  
Cosmic Inflation ◽  
The World

‘Frontiers of gravitational physics’ considers some of the issues involved in the theoretical description of gravity. Since 1915, it has been Einstein’s theory that has shaped our understanding of the gravitational interaction, but a lot has happened in the world of theoretical physics since then. Quantum mechanics, devised by Bohr, Heisenberg, and Schrödinger, is incompatible with gravity and so has raised numerous questions. Several theories, including String Theory and Loop Quantum Gravity, have been proposed with some success. The concepts of cosmic inflation, the cosmological constant, and the possibility of multiple universes are also discussed. It concludes that with further astrophysical studies a new fundamental theory may explain it all.

scholarly journals Quantum gravity: A brief history of ideas and some prospects

2015 ◽  
Vol 24 (11) ◽  
pp. 1530028 ◽  
Author(s):  
Steven Carlip ◽  
Dah-Wei Chiou ◽  
Wei-Tou Ni ◽  
Richard Woodard
Keyword(s):  
Black Hole ◽  
String Theory ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Black Hole Thermodynamics ◽  
History Of Ideas ◽  
Foreseeable Future ◽  
Gravitational Effects ◽  
History Of

We present a bird's-eye survey on the development of fundamental ideas of quantum gravity, placing emphasis on perturbative approaches, string theory, loop quantum gravity (LQG) and black hole thermodynamics. The early ideas at the dawn of quantum gravity as well as the possible observations of quantum gravitational effects in the foreseeable future are also briefly discussed.

Polymer quantization effects on gauge-flation

2018 ◽  
Vol 15 (10) ◽  
pp. 1850169
Author(s):  
M. Mardaani ◽  
K. Nozari
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Gauge Field ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Abelian Gauge ◽  
Friedmann Equations ◽  
Cosmological Inflation

Polymer quantum mechanics, as a non-standard representation of quantum mechanics, is based on a symmetric sector of loop quantum gravity known as loop quantum cosmology. In this work, by analyzing the Hamiltonian and Friedmann equations in the standard Hilbert space and polymer Hilbert space, we show that polymer quantization is a successful formalism for a non-Abelian gauge field driving the cosmological inflation, the so-called gauge-flation, in order to remove initial singularity and also keeping the inflationary trajectories in this model as attractors of dynamics after the bounce.

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

scholarly journals A quantized spacetime based on Spin(3,1) symmetry

2016 ◽  
Vol 25 (13) ◽  
pp. 1645004
Author(s):  
Pisin Chen ◽  
Hsu-Wen Chiang ◽  
Yao-Chieh Hu
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Generalized Uncertainty Principle ◽  
Spin Network ◽  
Fundamental Symmetry ◽  
New Type ◽  
Gravity Theories

We introduce a new type of the spacetime quantization based on the spinorial description suggested by loop quantum gravity. Specifically, we build our theory on a string theory inspired [Formula: see text] worldsheet action. Because of its connection with quantum gravity theories, our proposal may in principle link back to string theory, connect to loop quantum gravity where SU(2) is suggested as the fundamental symmetry, or serve as a Lorentzian spin network. We derive the generalized uncertainty principle and demonstrate the holographic nature of our theory. Due to the quantization of spacetime, geodesics in our theory are fuzzy, but the fuzziness is shown to be much below conceivable astrophysical bounds.

scholarly journals Dark energy and quantum gravity

2019 ◽  
Vol 28 (14) ◽  
pp. 1944018 ◽  
Author(s):  
Per Berglund ◽  
Tristan Hübsch ◽  
Djordje Minić
Keyword(s):  
Dark Energy ◽  
String Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Particle Physics ◽  
Dual Space ◽  
Planck Scale ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime

Realizing dark energy and the observed de Sitter spacetime in quantum gravity has proven to be obstructed in almost every usual approach. We argue that additional degrees of freedom of the left- and right-movers in string theory and a resulting doubled, noncommutatively generalized geometric formulation thereof can lead to an effective model of dark energy consistent with de Sitter spacetime. In this approach, the curvature of the canonically conjugate dual space provides for the dark energy inducing a positive cosmological constant in the observed spacetime, whereas the size of the above dual space is the gravitational constant in the same observed de Sitter spacetime. As a hallmark relation owing to a unique feature of string theory which relates short distances to long distances, the cosmological constant scale, the Planck scale and the effective TeV-sized particle physics scale must satisfy a see-saw-like formula — precisely the generic prediction of certain stringy cosmic brane type models.

scholarly journals CATEGORICAL FOUNDATION OF QUANTUM MECHANICS AND STRING THEORY

2009 ◽  
Vol 24 (06) ◽  
pp. 1175-1183 ◽  
Author(s):  
A. NICOLAIDIS
Keyword(s):  
Quantum Mechanics ◽  
String Theory ◽  
Category Theory ◽  
Mathematical Structure ◽  
Relational Algebra ◽  
Theoretical Physics ◽  
General Category ◽  
New Paradigm ◽  
Foundation Of Quantum Mechanics ◽  
Relational Logic

The unification of quantum mechanics and general relativity remains the primary goal of theoretical physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations of string theory, we analyze the relational logic developed by C. S. Peirce in the late 19th century. The Peircean logic has the mathematical structure of a category with the relation Rij among two individual terms Si and Sj, serving as an arrow (or morphism). We introduce a realization of the corresponding categorical algebra of compositions, which naturally gives rise to the fundamental quantum laws, thus indicating category theory as the foundation of quantum mechanics. The same relational algebra generates a number of group structures, among them W∞. The group W∞ is embodied and realized by the matrix models, themselves closely linked with string theory. It is suggested that relational logic and in general category theory may provide a new paradigm, within which to develop modern physical theories.

scholarly journals FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY

2007 ◽  
Vol 16 (09) ◽  
pp. 1397-1474 ◽  
Author(s):  
MUXIN HAN ◽  
YONGGE MA ◽  
WEIMING HUANG
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Quantum Dynamics ◽  
Loop Quantum Gravity ◽  
Hamiltonian Constraint ◽  
Dimensional Manifold ◽  
Fundamental Structure ◽  
Fundamental Scale

In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar–Isham–Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background-independent quantum gauge theories. There is no divergence within this background-independent and diffeomorphism-invariant quantization program of matter coupled to gravity.

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