scholarly journals Deformation quantization and the tomographic representation of quantum fields

2020 ◽  
Vol 17 (14) ◽  
pp. 2050217
Author(s):  
Jasel Berra-Montiel ◽  
Roberto Cartas-Fuentevilla
Keyword(s):  
Quantum Cosmology ◽  
Deformation Quantization ◽  
Loop Quantum Gravity ◽  
Star Product ◽  
Functional Integral ◽  
Loop Quantum Cosmology ◽  
Quantum Fields ◽  
Quantization Formalism ◽  
Tomographic Representation ◽  
Functional Integral Representation

The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic version of the Wigner map allows us to compute the symbols corresponding to field operators. Finally, the functional integral representation of the tomographic star product is determined. Some possible applications of the formalism to loop quantum cosmology and loop quantum gravity are 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 Equivalence of Models in Loop Quantum Cosmology and Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 41 ◽  
Author(s):  
Bekir Baytaş ◽  
Martin Bojowald ◽  
Sean Crowe
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Canonical Realization ◽  
Group Field Theory

The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.

DISSIPATIVE SCALAR FIELD THEORY VIA DEFORMATION QUANTIZATION

2013 ◽  
Vol 28 (16) ◽  
pp. 1350068
Author(s):  
ILIANA CARRILLO-IBARRA ◽  
HUGO GARCÍA-COMPEÁN ◽  
FRANCISCO J. TURRUBIATES
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Deformation Quantization ◽  
Star Product ◽  
Quantum Mechanical ◽  
Expectation Values ◽  
Scalar Field Theory ◽  
Oscillation Modes ◽  
Quantization Formalism ◽  
Damped Oscillation

The dissipative scalar field theory by means of the deformation quantization formalism is studied. Following the ideas presented by G. Dito and F. J. Turrubiates [Phys. Lett. A352, 309 (2006)] for quantum mechanics, a star product which contains the dissipative effect for the damped oscillation modes of the field is constructed. Employing this approach the expectation values of some observables in the quantum mechanical case as well as certain correlation functions for the field case are obtained under a particular dissipative process.

scholarly journals Quantum reduced loop gravity and the foundation of loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642005 ◽  
Author(s):  
Emanuele Alesci ◽  
Francesco Cianfrani
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Quantum Description ◽  
Semiclassical Dynamics ◽  
Loop Gravity ◽  
The Universe

Quantum reduced loop gravity is a promising framework for linking loop quantum gravity and the effective semiclassical dynamics of loop quantum cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.

scholarly journals Causal Poisson bracket via deformation quantization

2016 ◽  
Vol 13 (07) ◽  
pp. 1650104
Author(s):  
Jasel Berra-Montiel ◽  
Alberto Molgado ◽  
César D. Palacios-García
Keyword(s):  
Deformation Quantization ◽  
Star Product ◽  
Equations Of Motion ◽  
Virasoro Algebra ◽  
Bosonic String ◽  
Classical Solutions ◽  
Particle Model ◽  
Moyal Product ◽  
Quantization Formalism ◽  
Wick’S Theorem

Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced star-product is naturally related to the standard Moyal product through an appropriate causal Green’s functions connecting points in the space of classical solutions to the equations of motion. Our results resemble the Peierls–DeWitt bracket that has been analyzed in the multisymplectic context. Once our star-product is defined, we are able to apply the Wigner–Weyl map in order to introduce a generalized version of Wick’s theorem. Finally, we include some examples to explicitly test our method: the real scalar field, the bosonic string and a physically motivated nonlinear particle model. For the field theoretic models, we have encountered causal generalizations of the creation/annihilation relations, and also a causal generalization of the Virasoro algebra for the bosonic string. For the nonlinear particle case, we use the approximate solution in terms of the Green’s function, in order to construct a well-behaved causal bracket.

scholarly journals Some conceptual issues in loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642008 ◽  
Author(s):  
Aurélien Barrau ◽  
Boris Bolliet
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Symmetry Reduction ◽  
Loop Quantum Cosmology ◽  
Cosmological Perturbations ◽  
Quantum Spacetime ◽  
Open Issues

Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially critical when dealing with cosmological perturbations. The present paper reviews several approaches to the problem of building a consistent formalism that describes the dynamics of perturbations on a quantum spacetime and tries to address their respective strengths and weaknesses. We also review the main open issues in loop quantum cosmology.

scholarly journals Loop quantum gravity

2014 ◽  
Vol 24 (01) ◽  
pp. 1530005 ◽  
Author(s):  
Dah-Wei Chiou
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Black Hole Thermodynamics ◽  
Loop Quantum Cosmology ◽  
General Picture ◽  
Orderly Fashion ◽  
Introductory Review ◽  
Open Issues

This paper presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) — a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and systematic derivations, it aims to provide a general picture of LQG, placing emphasis on the fundamental ideas and their significance. The canonical formulation of LQG, as the central topic of the paper, is presented in a logically orderly fashion with moderate details, while the spin foam theory, black hole thermodynamics, and loop quantum cosmology are covered briefly. Current directions and open issues are also summarized.

Stability analysis of Einstein’s universe in loop quantum cosmology

2020 ◽  
Vol 35 (28) ◽  
pp. 2050166
Author(s):  
Eamon Mc Caughey
Keyword(s):  
General Relativity ◽  
Stability Analysis ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Hamiltonian Structure ◽  
Loop Quantum Cosmology ◽  
Universe Model ◽  
Integrals Of Motion ◽  
Cyclic Universe ◽  
The Stability

A stability analysis of Einstein’s universe in both classical general relativity and semiclassical loop quantum cosmology regimes is presented. The stability properties of the general relativity model are significantly altered due to loop quantum gravity corrections. Comparisons between both dynamical systems are considered on the basis of these modifications. The loop quantum cosmology solutions are restricted to an open universe model [Formula: see text] and represent a cyclic universe. The integrals of motion for both systems are found and their Hamiltonian structure determined.

scholarly journals Symmetry reduced loop quantum gravity: A bird’s eye view

2016 ◽  
Vol 25 (08) ◽  
pp. 1642010 ◽  
Author(s):  
Abhay Ashtekar
Keyword(s):  
Black Holes ◽  
Quantum Gravity ◽  
Early Universe ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Current Status ◽  
Loop Quantum Cosmology ◽  
Reduced Models ◽  
Quantum Aspects

This is a brief overview of the current status of symmetry reduced models in Loop Quantum Gravity. The goal is to provide an introduction to other more specialized and detailed reviews that follow. Since most of this work is motivated by the physics of the very early universe, I will focus primarily on Loop Quantum Cosmology and discuss quantum aspects of black holes only briefly.

Sign in / Sign up

Export Citation Format

Share Document