相关论文: ``Sum over Surfaces'' form of Loop Quantum Gravity

Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…

It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…

Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…

Boulatov and Ooguri have generalized the matrix models of 2d quantum gravity to 3d and 4d, in the form of field theories over group manifolds. We show that the Barrett-Crane quantum gravity model arises naturally from a theory of this type,…

We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G_{Newton} \Lambda) and extremely…

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…

Three-dimensional Lorentzian quantum gravity, expressed as the continuum limit of a nonperturbative sum over spacetimes, is tantalizingly close to being amenable to analytical methods, and some of its properties have been described in terms…

It is shown that the Riemannian curvature of the 3-dimensional hypersurfaces in space-time, described by the Wilson loop integral, can be represented by a quaternion quantum operator induced by the SU(2) gauge potential, thus providing a…

Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…

A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…

We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…

The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…

We study entanglement entropy in gravity theory with quantum effects. A simplest model is a two dimensional Einstein-Hilbert action . We use an $n$-sheet manifold to obtain an area term of entanglement entropy by summing over all background…

Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…

We summarize the basics of the loop representation of quantum gravity and describe the main aspects of the formalism, including its latest developments, in a reorganized and consistent form. Recoupling theory, in its graphical…

The role of the time surface term in the ADM Hamiltonian formulation of general relativity is investigated. We show that the variable contained in the time surface term (the scale factor) plays the role of a time-like variable. The…

This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…

"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…

We show that General Relativity can be formulated as a constrained topological theory for flat 2-connections associated to the Poincar\'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge…

We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…