Related papers: Discretization of 4d Poincar\'e BF theory: from gr…
Quadratic gravity in two dimensions can be formulated as a Background Field (BF) theory plus an interaction term which is polynomial in both, the gauge and Background fields. This formulation is similar to the one given by Freidel and…
We revise the classical continuum formulation behind the Spin Foam approach to the quantization of gravity. Based on the recent applications of the current EPRL-FK model beyond triangulations, we identify the tension with the implementation…
A dual formulation of group field theories, obtained by a Fourier transform mapping functions on a group to functions on its Lie algebra, has been proposed recently. In the case of the Ooguri model for SO(4) BF theory, the variables of the…
Recently it has been shown that the theory in the quadratic gauge on 4-sphere, $\mathbb{S}^{4}$ consists of two phases namely, the confined and the deconfined phases. A suitable finite field dependent BRST (FFBRST) transformation…
In this paper, we undertake the error analysis of the time discretization of systems of Forward-Backward Stochastic Differential Equations (FBSDEs) with drivers having polynomial growth and that are also monotone in the state variable. We…
In a recent paper, we introduced a new discretization scheme for gravity in 2+1 dimensions. Starting from the continuum theory, this new scheme allowed us to rigorously obtain the discrete phase space of loop gravity, coupled to…
3D Loop Quantum Gravity with a vanishing cosmological constant can be related to the quantization of the $\textrm{SU}(2)$ BF theory discretized on a lattice. At the classical level, this discrete model characterizes discrete flat geometries…
We provide the Barrett-Crane spin foam model for quantum gravity with a discrete action principle, consisting in the usual BF term with discretized simplicity constraints which in the continuum turn topological BF theory into gravity. The…
We demonstrate that the celebrated St$\ddot u$ckelberg formalism gets modified in the case of a massive four (3+1)-dimensional (4D) Abelian 2-form theory due to the presence of a self-duality discrete symmetry in the theory. The latter…
A theory for (1+3)-dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the…
We take the first steps in a systematic study of Group Field Theory renormalization, focusing on the Boulatov model for 3D quantum gravity. We define an algorithm for constructing the 2D triangulations that characterize the boundary of the…
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…
We perform the full Hamiltonian analysis of the topological BFCG action based on the Poincare 2-group. The Hamiltonian of the theory is constructed, and the algebra of constraints is computed. The Dirac brackets are evaluated, and the…
In 4 dimensions, general relativity can be formulated as a constrained $BF$ theory; we show that the same is true in 2 dimensions. We describe a spinfoam quantization of this constrained BF-formulation of 2d riemannian general relativity,…
Consider the group ${\mathbb{R}}^2$ with the discrete topology, and denote its Fourier algebra by $A({{\mathbb{R}}_{\rm d}^2})$. We reformulate a theorem of V.A. Yudin as a statement about restrictions of functions in $A({{\mathbb{R}}_{\rm…
We report a gravitational $BF$-type action principle propagating two (complex) degrees of freedom that, besides the gauge connection and the $B$ field, only employs an additional Lagrange multiplier. The action depends on two parameters and…
A detailed Dirac's canonical analysis for a topological four dimensional $BF$-like theory with a compact dimension is developed. By performing the compactification process we find out the relevant symmetries of the theory, namely, the full…
Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the GFT fields depend on variables associated to vertices of the associated simplicial…
We study the one-loop partition function of 3D gravity without cosmological constant on the solid torus with arbitrary metric fluctuations on the boundary. To this end we employ the discrete approach of (quantum) Regge calculus. In contrast…
We perform a complete Hamiltonian analysis of the BFCG action for a general Lie 2-group by using the Dirac procedure. We show that the resulting dynamical constraints eliminate all local degrees of freedom which implies that the BFCG theory…