Related papers: Loop Variable Representation of Classical Higher D…
The scalar-tensor theories of gravity in spacetime dimensions $D+1>2$ are studied. By doing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the…
A nonperturbative approach to quantum gravity that has generated much discussion is the attempt to construct a ``loop representation." Despite it's success in linear quantum theories and a part of 2+1 quantum gravity, it has recently been…
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…
We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified…
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or…
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the…
To appear in proceedings of II Workshop on ``Constraints Theory and Quantisation Methods''Montepulciano (Siena) 1993} General discussion of the constraints of 2+1 gravity, with emphasis on two approaches, namely the second order and first…
We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
The two-dimensional effective Polyakov action is often realized as the anomalous contributions of string theories and fermions coupled to gravity in two-dimensions. However, as a result of the reparameterization invariance, one finds that…
In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and…
We study several aspects of the canonical quantization of supergravity in terms of the Asthekar variables. We cast the theory in terms of a $GSU(2)$ connection and we introduce a loop representation. The solution space is similar to the…
New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum…
We discuss the semiclassical limit of Quantum Reduced Loop Gravity, a recently proposed model to address the quantum dynamics of the early Universe. We apply the techniques developed in full Loop Quantum Gravity to define the semiclassical…
A starting point for the present work was the statement recently discussed in the literature that two Hamiltonian formulations for the theory of gravity, the one proposed by Dirac and the other by Arnowitt - Deser - Misner, may not be…
We construct a new vacuum for loop quantum gravity, which is dual to the Ashtekar-Lewandowski vacuum. Because it is based on BF theory, this new vacuum is physical for $(2+1)$-dimensional gravity, and much closer to the spirit of spin foam…
The 3+1 (ADM) formulation of General Relativity is used in, for example, canonical quantum gravity and numerical relativity. Here we present a 3+1 decomposition of the minimal Standard-Model Extension gravity Lagrangian. By choosing the…
We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\mu\nu}$ in…
We consider the issue of attaining a consistent Hamiltonian formulation, after a 3+1 splitting, of a well defined action principle for asymptotically flat gravity. More precisely, our starting point is the gravitational first order Holst…
The canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to be a dynamical, fluctuating quantity in quantum gravity. After presenting…