Related papers: Introduction to Causal Fermion Systems
Causal systems describe the localizability of relativistic quantum systems complying with the principles of special relativity and elementary causality. At their classification we restrict ourselves to real mass and finite spinor systems.…
A microscopic theory is presented for identifying shape-phase structures and transitions in interacting fermion systems. The method provides a microscopic description for collective shape-phases, and reveals detailed dependence of such…
This is intended to be a very basic introduction and short (and of course incomplete) overview of thermal field theory. In the first part, I introduce the thermal propagator at a very simple level and give the Feynman rules using the…
We give a broad overview of a construction of a theory for matter on fixed causal set backgrounds. We introduce the Sorkin-Johnston formalism for a free (real) scalar field theory that is applicable to regions of continuum spacetimes as…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
This paper introduces Whittemore, a language for causal programming. Causal programming is based on the theory of structural causal models and consists of two primary operations: identification, which finds formulas that compute causal…
The two fields of machine learning and graphical causality arose and developed separately. However, there is now cross-pollination and increasing interest in both fields to benefit from the advances of the other. In the present paper, we…
A new mechanism is proposed to explain the appearance of the three known fermion generations in a natural way. The underlying idea is based on the discreteness of the spectrum of solutions of the gap equation appearing in models of…
In this essay, we explore the geometric structures involved in the Wolfram model of fundamental physics. Furthermore, we propose some directions of research aiming to get the bosons and fermions out of this framework.
The study of entanglement in systems composed of identical particles raises interesting challenges with far-reaching implications in both, our fundamental understanding of the physics of composite quantum systems, and our capability of…
The emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski space. After a brief recap of the Dirac equation and its solution space, in order to allow for the…
Causal theory is now widely developed with many applications to medicine and public health. However within the discipline of reliability, although causation is a key concept in this field, there has been much less theoretical attention. In…
Causal set theory provides a model of discrete spacetime in which spacetime events are represented by elements of a causal set---a locally finite, partially ordered set in which the partial order represents the causal relationships between…
A spherical system is a combinatorial object, arising in the theory of wonderful varieties, defined in terms of a root system. All spherical systems can be obtained by means of some general combinatorial procedures (such as parabolic…
This article presents the most interesting philosophical issues as they arise in causal set theory. The first concerns the apparent disappearance of spacetime at the fundamental level. It shows how the looming empirical incoherence is…
We discuss the origin of causal set structure and the emergence of classical space and time in the universe. Given that the universe is a closed self-referential quantum automaton with a quantum register consisting of a vast number of…
Complex systems have interested researchers across a broad range of fields for many years and as computing has become more accesible and feasible, it is now possible to simulate aspects of these systems. A major point of research is how…
We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…
Causal reasoning is a crucial part of science and human intelligence. In order to discover causal relationships from data, we need structure discovery methods. We provide a review of background theory and a survey of methods for structure…
Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions…