Related papers: Spin Networks and Quantum Gravity
The flat, homogeneous, and isotropic universe with a massless scalar field is a paradigmatic model in Loop Quantum Cosmology. In spite of the prominent role that the model has played in the development of this branch of physics, there still…
We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity, in a large subspace of the model's kinematic Hilbert space which is the space of…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
We study the existence and limitations for hyperinvariant tensor networks incorporating a local SU(2) symmetry. As discrete implementations of the anti de-Sitter/conformal field theory (AdS/CFT) correspondence, such networks have created…
While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define the concept of a `spin foam' going from one spin…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of…
We present the construction of a new state sum model for $4d$ Lorentzian quantum gravity based on the description of quantum simplicial geometry in terms of edge vectors. Quantum states and amplitudes for simplicial geometry are built from…
A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to…
Recently the $\text{SU}(2)$ spin-network states in loop quantum gravity is generalized to those of the corresponding affine Lie algebra. We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure…
This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path…
Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine the structure of the…
We describe fundamental equations which define the topological ground states in the lattice realization of the SU(2) BF phase. We introduce a new scalar Hamiltonian, based on recent works in quantum gravity and topological models, which is…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
We construct a class of spin foam models describing matter coupled to gravity, such that the gravitational sector is described by the unitary irreducible representations of the appropriate symmetry group, while the matter sector is…
We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach…