3GPP2/802.20 RC/QC-LDPC encoding

Abelian Ashtekar formulation from the ADM action

“…where β is an arbitrary constant that corresponds to the Immirzi parameter of the "full" theory [15,17,18]. The linearized variablesà j a and e a i are canonical, as we shall show.…”

“…Nevertheless, such approaches seem to fail due to the lack of renormalizability [10].An alternative to build a quantum theory of gravity that avoids the renormalizability problems is provided by Loop Quantum Gravity (LQG). This formulation may be obtained by applying the Dirac method to the Einstein theory in order to bring it into a canonical form, then, the phase space is parameterized by the Ashtekar variables [11][12][13][14][15][16][17][18][19]. These variables are a SU (2) connection A i a and a densitised triad E a i , which is a vector with respect to SU (2) and a density of weight one [15][16][17][18] (here, the first letters of the alphabet label space coordinates and those belonging to the middle of the alphabet are SU(2) indexes).…”

“…This formulation may be obtained by applying the Dirac method to the Einstein theory in order to bring it into a canonical form, then, the phase space is parameterized by the Ashtekar variables [11][12][13][14][15][16][17][18][19]. These variables are a SU (2) connection A i a and a densitised triad E a i , which is a vector with respect to SU (2) and a density of weight one [15][16][17][18] (here, the first letters of the alphabet label space coordinates and those belonging to the middle of the alphabet are SU(2) indexes). The phase space becomes that of a conventional SU (2) Yang-Mills theory except by the fact that besides the Yang-Mills Gauss constraint, that generates SU (2) gauge transformations, there appear two more constraints: the vectorial constraint generating 3-dimensional space diffeomorphisms and the scalar or Hamiltonian constraint, which generates time diffeomorphisms [17,18].…”

Evolution ofΛblack holes in the minisuperspace approximation of loop quantum gravity

“…(For a review, the interested reader is referred to [1][2][3][4][5] and references therein.) Loop quantum gravity has already been successful in answering the question of the origin of black hole entropy [6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Cosmic recall and the scattering picture of loop quantum cosmology

“…The results initially obtained numerically for the flat isotropic model with massless scalar field [6,7] were shown to be general features of that model [8,9] and next extended to more general matter fields [10][11][12] and topologies [13,14] as well as to less symmetric systems: anisotropic [15][16][17][18][19][20][21] and some classes of the inhomogeneous ones [22]. Also, although the theory originates from the canonical framework, a connection with the spin foam [23] models was made through the studies of the path integral in LQC [24] as well as the analysis of the cosmological models within the spin foam models themselves [25]. Another avenue of extensions is the perturbation theory around the cosmological solutions [26].…”