scholarly journals Loop Quantization of a 3D AbelianBFModel withσ-Model Matter

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Diego C. M. Mendonça ◽  
Olivier Piguet
Keyword(s):  
Hilbert Space ◽  
Quantum Gravity ◽  
Sigma Model ◽  
Loop Quantum Gravity ◽  
Present Model ◽  
Scalar Fields ◽  
Background Independence ◽  
Loop Quantization

The main goal of this work is to explore the symmetries and develop the dynamics associated with a 3D AbelianBFmodel coupled to scalar fields submitted to a sigma model like constraint, at the classical and quantum levels. Background independence, on which the model is founded, strongly constrains its nature. We adapt to the present model the techniques of Loop Quantum Gravity in order to construct its physical Hilbert space and its observables.

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 Shape dynamical loop gravity from a conformal Immirzi parameter

2017 ◽  
Vol 26 (11) ◽  
pp. 1750131 ◽  
Author(s):  
Patrick J. Wong
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Three Dimensional ◽  
Classical Level ◽  
Spatial Geometry ◽  
Loop Quantization ◽  
Loop Gravity ◽  
Precise Interpretation ◽  
Gauge Connection ◽  
Area And Volume

The Immirzi parameter of loop quantum gravity is a one-parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum theory as it appears in the spectra of geometric operators, despite being irrelevant at the classical level. The parameter’s appearance in the area and volume spectra to the same power as the Planck area suggest that it plays a role in determining the fundamental length scale of space. In fact, a consistent interpretation is that it represents a constant rescaling of the kinematical spatial geometry. An interesting realization is that promoting the Immirzi parameter to be a general conformal transformation leads to a system which can be identified as analogous to the linking theory of shape dynamics. A three-dimensional gravitational gauge connection is then constructed within the linking theory in a manner analogous to loop quantum gravity, thereby facilitating the application of the established procedure of loop quantization.

scholarly journals Space–Time Physics in Background-Independent Theories of Quantum Gravity

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 251
Author(s):  
Martin Bojowald
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Riemannian Geometry ◽  
Loop Quantum Gravity ◽  
Space Time ◽  
Time Analysis ◽  
Complete Space ◽  
Background Independence ◽  
Starting Point

Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine not only the dynamics of space–time but also its geometry, which may have equally important implications for claims of potential physical observations. One of the leading candidates for background-independent quantum gravity is loop quantum gravity. By combining and interpreting several recent results, it is shown here how the canonical nature of this theory makes it possible to perform a complete space–time analysis in various models that have been proposed in this setting. In spite of the background-independent starting point, all these models turned out to be non-geometrical and even inconsistent to varying degrees, unless strong modifications of Riemannian geometry are taken into account. This outcome leads to several implications for potential observations as well as lessons for other background-independent approaches.

scholarly journals Quantum groups and polymer quantum mechanics

2021 ◽  
Author(s):  
G. Acquaviva ◽  
A. Iorio ◽  
L. Smaldone
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Quantum Groups ◽  
Loop Quantum Gravity ◽  
Quantization Scheme ◽  
Creation And Annihilation Operators

In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well defined on the Hilbert space [Formula: see text]. It is henceforth deemed impossible to define standard creation and annihilation operators. In this paper, we show that a [Formula: see text]-oscillator structure, and hence [Formula: see text]-deformed creation/annihilation operators, can be naturally defined on [Formula: see text], which is then mapped into the sum of many copies of the [Formula: see text]-oscillator Hilbert space. This shows that the [Formula: see text]-calculus is a natural calculus for Polymer Quantum Mechanics. Moreover, we show that the inequivalence of different superselected sectors of [Formula: see text] is of topological nature.

scholarly journals Separable Hilbert space in loop quantum gravity

2004 ◽  
Vol 45 (7) ◽  
pp. 2802-2814 ◽  
Author(s):  
Winston Fairbairn ◽  
Carlo Rovelli
Keyword(s):  
Hilbert Space ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Separable Hilbert Space

scholarly journals Review on hermiticity of the volume operators in Loop Quantum Gravity

2019 ◽  
Vol 51 (5) ◽  
Author(s):  
S. Ariwahjoedi ◽  
I. Husin ◽  
I. Sebastian ◽  
F. P. Zen
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity

scholarly journals Effective Scalar Potential in Asymptotically Safe Quantum Gravity

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 45
Author(s):  
Christof Wetterich
Keyword(s):  
Quantum Gravity ◽  
Top Quark ◽  
Particle Physics ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Standard Model ◽  
Scaling Potential ◽  
Realistic Description ◽  
The Masses ◽  
Dynamical Dark Energy

We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing “cosmological constant” or dynamical dark energy.

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