Results 1  10
of
14
Dynamics of scalar field in polymerlike representation
"... In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scala ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism invariant Hilbert space, which is both selfadjoint and positive. On the other hand, the Hamiltonian constraint operator for the scalar field coupled to gravity can be well defined in the coupled kinematical Hilbert space. There are 1parameter ambiguities due to scalar field in the construction of both operators. The results heighten our confidence that there is no divergence within this background independent and diffeomorphism invariant quantization approach of matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the master constraint programme can be carried out in this coupled system by employing a selfadjoint master constraint operator on the diffeomorphism invariant Hilbert space.
The Hilbert space of ChernSimons theory on the cylinder. A Loop Quantum Gravity approach
, 2009
"... We consider the canonical quantization of threedimensional ChernSimons theory on a space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and solve them, thus constructing the gauge a ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
We consider the canonical quantization of threedimensional ChernSimons theory on a space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and solve them, thus constructing the gauge and diffeomorphism invariant physical Hilbert space of the theory. This space is infinite dimensional, but separable. 1
QuasiLocal Energy in Loop Quantum Gravity
, 812
"... Although there is no known meaningful notion of the energy density of the gravitational field in general relativity, a few notions of quasilocal energy of gravity associated to extended but finite domains have been proposed. In this paper, the notions of quasilocal energy are studied in the framew ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Although there is no known meaningful notion of the energy density of the gravitational field in general relativity, a few notions of quasilocal energy of gravity associated to extended but finite domains have been proposed. In this paper, the notions of quasilocal energy are studied in the framework of loop quantum gravity, in order to see whether these notions can be carried out at quantum level. Two basic quasilocal geometric quantities are quantized, which lead to welldefined operators in the kinematical Hilbert space of loop quantum gravity. We then use them as basic building blocks to construct different versions of quasilocal energy operators. The operators corresponding to BrownYork energy, LiuYau energy, Hawking energy, and Geroch energy are obtained respectively. The virtue of the Geroch energy operator is beneficial for us to derive a rather general entropyarea relation from loop quantum gravity. PACS number(s): 04.60.Pp, 04.20.Cv 1
Semiclassical states in homogeneous loop quantum cosmology
 Class. Quantum Grav
, 2006
"... Semiclassical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semiclassical (coherent) state is obtained by solving the eigenequation of that operator. Moreo ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Semiclassical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semiclassical (coherent) state is obtained by solving the eigenequation of that operator. Moreover, we use these coherent states to analyze the semiclassical limit of the quantum dynamics. It turns out that the Hamiltonian constraint operator employed currently in homogeneous LQC has correct classical limit with respect to the coherent states. In the second approach, the other kind of semiclassical state is derived from the mathematical construction of coherent states for compact Lie groups due to Hall.
Probable Entropic Nature of Gravity in Ultraviolet and Infrared LimitsPart I: An Ultraviolet Case
"... This work presents a study of the possibility for extending the wellknown results of E. Verlinde concerning the entropic nature of gravity to the ultraviolet region (Planck's energies) and also the derivation of quantum corrections to Einstein Equations. ..."
Abstract
 Add to MetaCart
This work presents a study of the possibility for extending the wellknown results of E. Verlinde concerning the entropic nature of gravity to the ultraviolet region (Planck's energies) and also the derivation of quantum corrections to Einstein Equations.
Master Constraint Operator in Loop Quantum Gravity
, 2008
"... We introduce a Master Constraint Operator ˆ M densely defined in the diffeomorphism invariant Hilbert space in loop quantum gravity. The corresponding quadratic form coincides with the one proposed by Thiemann in the master constraint programme. It is shown that ˆ M is positive and symmetric, and he ..."
Abstract
 Add to MetaCart
(Show Context)
We introduce a Master Constraint Operator ˆ M densely defined in the diffeomorphism invariant Hilbert space in loop quantum gravity. The corresponding quadratic form coincides with the one proposed by Thiemann in the master constraint programme. It is shown that ˆ M is positive and symmetric, and hence has its Friedrichs selfadjoint extension. So the master constraint programme for loop quantum gravity can be carried out in principle by employing ˆ M.
Introduction to Loop Quantum Cosmology
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2012
"... ..."
(Show Context)
Anomalyfree representations of the holonomyflux algebra
, 2008
"... We work on the uniqueness [1] of representations of the holonomyflux algebra in loop quantum gravity. We argue that for analytic diffeomorphisms, the flux operators can be only constants as functions on the configuration space in representations with no anomaly, which are zero in the standard repre ..."
Abstract
 Add to MetaCart
(Show Context)
We work on the uniqueness [1] of representations of the holonomyflux algebra in loop quantum gravity. We argue that for analytic diffeomorphisms, the flux operators can be only constants as functions on the configuration space in representations with no anomaly, which are zero in the standard representation. In loop quantum gravity 1, the configuration variables are holonomies he[A] of a connection field and the momentum variables are surface integrals E(S, f) of a triad field. Quite interestingly, the Poisson brackets between the momentum variables do not vanish. The origin of this noncommutativity comes from the twodimensional singular smearing of E(S, f) [3] and E(S, f) can be understood as some vector fields X(S, f) on the configuration space A. In the standard representation, every holonomy operator is multiplication and every flux operator is derivation on the Hilbert space L2 ( Ā, µ) [4]. Representations of the holonomyflux algebra were further investigated in [5]. It was motivated by the fact that the momentum variables E(S, f) are not constants 2 on