Related papers: Causal Fermion Systems: A Primer for Lorentzian Ge…
We compare the structures and methods in the theory of causal fermion systems with generalized trace dynamics and non-commutative geometry. Although the three theories differ on many aspects, they agree in that the geometric structure to be…
In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present…
I present a scheme of drawing causal diagrams based on physically motivated mathematical models expressed in terms of temporal differential equations. They provide a means of better understanding the processes and causal relationships…
We discuss the usual account of causal structure that relies on the temporal precedence constraint between cause-effect pairs. In particular, we consider the subtle interplay between local and global characters of time and causality encoded…
We construct a family of closeness functions on the space of finite volume Lorentzian geometries using the abundance of discrete intervals in the underlying random causal sets. Although strictly weaker than a Lorentzian Gromov-Hausdorff…
The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interesting mathematics that has arisen in connection with the causal…
In General Relativity the metric can be recovered from the structure of the lightcones and a measure giving the volume element. Since the causal structure seems to be simpler than the Lorentzian manifold structure, this suggests that it is…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…
Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms.…
We present some modern theories on the structure of spacetime that can be classified as relational theories in the direction of Leibniz's ontology. In order to analyze the nature of spacetime we consider three levels of knowledge…
We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The r\^ole of the metric is taken over by the time separation function, in terms of which all basic notions are…
Some links between Lorentz and Finsler geometries have been developed in the last years, with applications even to the Riemannian case. Our purpose is to give a brief description of them, which may serve as an introduction to recent…
After sketching a context in which to seek observable signals of spatio-temporal discreteness, I briefly review the status of the causal set program for quantum gravity, concluding with a simple model for the field produced by a moving…
Causal discovery algorithms allow for the inference of causal structures from probabilistic relations of random variables. A natural field for the application of this tool is quantum mechanics, where a long-standing debate about the role of…
This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking…
This write-up starts by introducing lattice chirality to people possessing a fairly modern mathematical background, but little prior knowledge about modern physics. I then proceed to present two new and speculative ideas.
We derive all possible causality conditions for conformally flat Lorentzian metrics on the two-dimensional cylinder.
We give a simple model to explain the origin of fermion families, and chirality through the use of a domain wall placed in a five dimensional space-time.
The natural topological, differentiable and geometrical structures on the space of light rays of a given spacetime are discussed. The relation between the causality properties of the original spacetime and the natural structures on the…