Related papers: Path integral measure and triangulation independen…
A formulation of discrete gravity was recently proposed based on defining a lattice and a shift operator connecting the cells. Spinors on such a space will have rotational SO(d) invariance which is taken as the fundamental symmetry.…
We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as integrals over the SL(2, R) invariant Gaussian functional measure. We reduce these path integrals to the products of Wiener path…
A key insight used in developing the theory of Causal Dynamical Triangulations (CDTs) is to use the causal (or light-cone) structure of Lorentzian manifolds to restrict the class of geometries appearing in the Quantum Gravity (QG) path…
This paper proposes a definition of gravitational observables and of their path integral formula within the framework of ADM foliation and the choice of unimodular gauge classes. The method enforces a BRST invariant gauge fixing of the…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model…
A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
A powerful strategy to treat quantum field theories beyond perturbation theory is by putting them on a lattice. However, the dynamical and symmetry structure of general relativity have for a long time stood in the way of a well-defined…
We conduct numerical simulations of a model of four dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume the model contains a…
In this note we propose a topological action for a Poincare times diffeomorphism invariant gauge theory. We show that there is Higgs phase where the gauge symmetry is spontaneous broken to a diagonal Lorentz subgroup and gives the…
By regularizing the singularities appearing in the two dimensional Regge calculus by means of a segment of a sphere or pseudo-sphere and then taking the regulator to zero, we obtain a simple formula for the gauge volume which appears in the…
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional…
Using the invariance of Quadratic Gravity in FLRW metric under the group of diffeomorphisms of the time coordinate, we rewrite the action $A$ of the theory in terms of the invariant dynamical variable $g(\tau)\,.$ We propose to consider the…
The action $A$ of Quadratic Gravity in FLRW metric is invariant under the group of diffeomorphisms of the time coordinate and can be written in terms of the only dynamical variable $g(\tau)\,.$ We construct perturbation theory for…
The use in the action integral of a volume element of the form $\Phi d^{D}x$ where $\Phi$ is a metric independent measure can give new interesting results in all types of known generally coordinate invariant theories: (1) 4-D theories of…
We discuss the discretization of Yang-Mills theories on Dynamical Triangulations in the compact formulation, with gauge fields living on the links of the dual graph associated with the triangulation, and the numerical investigation of the…
We consider spinfoam quantum gravity for general triangulations in the regime $l_P^2\ll a\ll a/\gamma$, namely in the combined classical limit of large areas $a$ and flipped limit of small Barbero-Immirzi parameter $\gamma$, where $l_P$ is…
We study numerically the dynamical triangulation formulation of two-dimensional quantum gravity using a restricted class of triangulation, so-called minimal triangulations, in which only vertices of coordination number 5, 6, and 7 are…
We propose a Lagrangian path integral based on gauge symmetries generated by a symmetric higher-order $\Delta$-operator, and demonstrate that this path integral is independent of the chosen gauge-fixing function. No explicit change of…