相关论文: Polyhedra in loop quantum gravity

In the prequel of this paper, Kauffman and Ogasa introduced new topological quantum invariants of compact oriented 3-manifolds with boundary where the boundary is a disjoint union of two identical surfaces. The invariants are constructed…

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…

In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint. On this Hilbert space, using the methods of Thiemann, we obtain a family…

A fundamental motif in frustrated magnetism is the fully mutually coupled cluster of $N$ spins, with each spin coupled to every other spin. Clusters with $N=2$ and $3$ have been extensively studied as building blocks of square and…

A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the…

The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…

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…

The intention of this thesis is to provide general tools and concepts that allow to perform a mathematically substantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum…

Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We…

We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological…

We develop the quantization of unimodular gravity in the Plebanski and Ashtekar formulations and show that the quantum effective action defined by a formal path integral is unimodular. This means that the effective quantum geometry does not…

We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian…

We investigate the generalization of loop gravity's twisted geometries to a q-deformed gauge group. In the standard undeformed case, loop gravity is a formulation of general relativity as a diffeomorphism-invariant SU(2) gauge theory. Its…

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a…

Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…

In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, one restricts oneself to families of paths admitting only finite number of isolated…

We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…

A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space…

A recent study by Bojowald and Paily provided a path toward the identification of an effective quantum-spacetime picture of Loop Quantum Gravity, applicable in the "Minkowski regime", the regime where the large-scale (coarse-grained)…

Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…