Related papers: Graph kinematics of discrete physical objects: bey…
Recently, Apers and Piddock [TQC '23] strengthened the connection between quantum walks and electrical networks via Kirchhoff's Law and Ohm's Law. In this work, we develop a new multidimensional electrical network by defining Alternative…
It is shown that nonzero orbital momentum in the vertex of secondary interaction in the triangle graph leads to a more clear picture corresponding to the moving complex singularity compared with the case of constant vertex. The peak in the…
In 1966, Cummins introduced the "tree graph": the tree graph $\mathbf{T}(G)$ of a graph $G$ (possibly infinite) has all its spanning trees as vertices, and distinct such trees correspond to adjacent vertices if they differ in just one edge,…
This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and…
Motivated by quantum mechanical considerations we earlier suggested an alternative action for discretised quantum gravity which has a dimension of length. It is the so called "linear" action. The proposed action is a "square root" of the…
We prove a neat factorization property of Feynman graphs in covariant perturbation theory. The contribution of the graph to the effective action is written as a product of a massless scalar momentum integral that only depends on the basic…
The behaviour of two-loop two-point diagrams at non-zero thresholds corresponding to two-particle cuts is analyzed. The masses involved in a cut and the external momentum are assumed to be small as compared to some of the other masses of…
We introduce a discrete 4-dimensional module over the integers that appears to have maximal symmetry. By adjoining the usual Minkowski distance, we obtain a discrete 4-dimensional Minkowski space. Forming universe histories in this space…
While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define the concept of a `spin foam' going from one spin…
Previous work established a universal form for the equation of motion of small bodies in theories of a metric and other tensor fields that have second-order field equations following from a covariant Lagrangian in four spacetime dimensions.…
Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the…
A discretisation of differential geometry using the Whitney forms of algebraic topology is consistently extended via the introduction of a pairing on the space of chains. This pairing of chains enables us to give a definition of the…
Temporal graphs are graphs where the presence or properties of their vertices and edges change over time. When time is discrete, a temporal graph can be defined as a sequence of static graphs over a discrete time span, called lifetime, or…
A monotone drawing of a graph G is a straight-line drawing of G such that every pair of vertices is connected by a path that is monotone with respect to some direction. Trees, as a special class of graphs, have been the focus of several…
The Euclidean Steiner tree problem asks to find a min-cost metric graph that connects a given set of \emph{terminal} points $X$ in $\mathbb{R}^d$, possibly using points not in $X$ which are called Steiner points. Even though near-linear…
The three standard products (the Cartesian, the direct and the strong product) of undirected graphs have been wellinvestigated, unique prime factor decomposition (PFD) are known and polynomial time algorithms have been established for…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
The equations defining pure spinors are interpreted as equations of motion formulated on the lightcone of a ten-dimensional, lorentzian, momentum space. Most of the equations for fermion multiplets, usually adopted by particle physics, are…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
We highlight a topological aspect of the graph limit theory. Graphons are limit objects for convergent sequences of dense graphs. We introduce the representation of a graphon on a unique metric space and we relate the dimension of this…