Related papers: Discretization of 4d Poincar\'e BF theory: from gr…
The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four dimensional spacetime. The presence of a boundary breaks the Ward identities which describe the gauge symmetries of the theory, and, using standard…
Derivative boundary conditions introduce challenges for mesh-free discretizations of PDEs on surfaces, especially when the domain is represented by randomly sampled point clouds. The recently developed two-step tangent-space RBF-generated…
We study generalizations of 3- and 4-dimensional BF-theory in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of…
We compare two theoretical approaches to dielectric diblock copolymer melts in an external electric field. The first is a relatively simple analytic expansion in the relative copolymer concentration, and includes the full electrostatic…
A formalism is developed to study certain five-term recursion relations by discrete phase integral (or Wentzel-Kramers-Brillouin) methods. Such recursion relations arise naturally in the study of the Schrodinger equation for certain spin…
This paper presents a fast "two-dimensional Fourier Continuation" (2D-FC) method for the construction of biperiodic extensions of smooth, non-periodic functions defined over general two-dimensional (2D) domains, including domains with…
The Jackiw-Teitelboim model written as a BF theory in two dimensions is analyzed by using the Dirac's and Faddeev-Jackiw formalism. The analysis consists in finding the full structure of the constraints, the gauge transformations, the…
A direct relation between two types of topological field theories, Chern-Simons theory and BF theory, is presented by using ``Generalized Differential Calculus'', which extends an ordinary p-form to an ordered pair of p and (p+1)-form. We…
In the context of quantum gravity, group field theories are field theories that generate spinfoam amplitudes as Feynman diagrams. They can be understood as generalizations of the matrix models used for 2d quantum gravity. In particular…
This paper presents a new reformulated theorem for fields embedded on a sphere or a disk. We focus in particular on the associated sphere of a disk when closing its only one boundary. We call this the disk-sphere duality theorem for the…
We derive the the Barrett-Crane spin foam model for Euclidean 4 dimensional quantum gravity from a discretized BF theory, imposing the constraints that reduce it to gravity at the quantum level. We obtain in this way a precise prescription…
We propose a fully discrete finite volume scheme for the standard Fokker-Planck equation. The space discretization relies on the well-known square-root approximation, which falls into the framework of two-point flux approximations. Our time…
In this article we explain discrete torsion. Put simply, discrete torsion is the choice of orbifold group action on the B field. We derive the classification H^2(G, U(1)), we derive the twisted sector phases appearing in string loop…
We consider a two-phase Darcy flow in a fractured and deformable porous medium for which the fractures are described as a network of planar surfaces leading to so-called hybrid-dimensional models. The fractures are assumed open and filled…
The kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
We present a dual 5D braneworld picture of a recently suggested model for a microcanonical description of a 4D cosmology driven by a conformal field theory with a large number of quantum fields. The 5D side of the duality relation is…
Lattice actions and amplitudes that perfectly mirror continuum physics are known as perfect discretizations. Such perfect discretizations naturally preserve the symmetries of the continuum. This is a key concern for general relativity,…
In this thesis I studied the Symanzik's method for the introduction of the boundary in a field theory and, specifically, I applied this method to three Topological Field Theories of the Shwartz type: the non-abelian Chern-Simons model, the…
We use holography to study the spectra of boundary conformal field theories (BCFTs). To do so, we consider a 2-dimensional Euclidean BCFT with two circular boundaries that correspond to dynamical end-of-the-world branes in 3-dimensional…