scholarly journals Hilbert space structure of covariant loop quantum gravity

2002 ◽  
Vol 66 (2) ◽  
Author(s):  
Sergei Alexandrov
Keyword(s):  
Hilbert Space ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Space Structure

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 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 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.

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 Clock-dependent spacetime

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sung-Sik Lee
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Gravity ◽  
Hilbert Spaces ◽  
Coordinate Systems ◽  
Physical Laws

Abstract Einstein’s theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.

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