Related papers: Polytopes in all dimensional loop quantum gravity
Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…
This is the third in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin…
Generalized Quasitopological Gravities (GQTGs) are higher-order extensions of Einstein gravity in $D$ dimensions satisfying a number of interesting properties, such as possessing second-order linearized equations of motion on top of…
Motivated by the quantum speedup for dynamic programming on the Boolean hypercube by Ambainis et al. (2019), we investigate which graphs admit a similar quantum advantage. In this paper, we examine a generalization of the Boolean hypercube…
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved…
4-dimensional $A_{4}$ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(A_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an…
We discuss the structure of Dyson--Schwinger equations in quantum gravity and conclude in particular that all relevant skeletons are of first order in the loop number. There is an accompanying sub Hopf algebra on gravity amplitudes…
The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth…
We study the extension complexity of polytopes with few vertices or facets. On the one hand, we provide a complete classification of $d$-polytopes with at most $d+4$ vertices according to their extension complexity: Out of the…
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…
Among the usual constraints of (1,1) supergravity in d=2 the condition of vanishing bosonic torsion is dropped. Using the inverse supervierbein and the superconnection considerably simplifies the formidable computational problems. It allows…
We investigate a novel setting for polytope rigidity, where a flex must preserve edge lengths and the planarity of faces, but is allowed to change the shapes of faces. For instance, the regular cube is flexible in this notion. We present…
Over the last decade there were significant advances in the understanding of quantum gravity coupled to point particles in 3D (2+1-dimensional) spacetime. Most notably it is emerging that the theory can be effectively described as a theory…
The quadratic gravity constraints are reformulated in terms of the Newman-Penrose-like quantities. In such a frame language, the field equations represent a linear algebraic system for the Ricci tensor components. In principle, a procedure…
It has been suggested that higher-derivative gravity theories coupled to a scalar field with shift symmetry may be an important candidate for a quantum gravity. We show that this class of gravity theories are renormalizable in D = 3 and 4…
We study canonical quantization of a class of 2d dilaton gravity models, which contains the model proposed by Callan, Giddings, Harvey and Strominger. A set of non-canonical phase space variables is found, forming an $SL(2,{\bf R}) \times…
We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…
A one-parameter class of simple models of two-dimensional dilaton gravity, which can be exactly solved including back-reaction effects, is investigated at both classical and quantum levels. This family contains the RST model as a special…
We relate three-dimensional loop quantum gravity to the combinatorial quantisation formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant. We compare the…
Two dimensional gravity with torsion is proved to be equivalent to special types of generalized 2d dilaton gravity. E.g. in one version, the dilaton field is shown to be expressible by the extra scalar curvature, constructed for an…