Related papers: Causal Fermion Systems: An Introduction to Fundame…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
Causal modelling is a tool for generating causal explanations of observed correlations and has led to a deeper understanding of correlations in quantum networks. Existing frameworks for quantum causality tend to focus on acyclic causal…
Fermions are fundamental particles which obey seemingly bizarre quantum-mechanical principles, yet constitute all the ordinary matter that we inhabit. As such, their study is heavily motivated from both fundamental and practical incentives.…
Mathematical models are fundamental building blocks in the design of dynamical control systems. As control systems are becoming increasingly complex and networked, approaches for obtaining such models based on first principles reach their…
It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
Deeper insight leads to better practice. We show how the study of the foundations of quantum mechanics has led to new pictures of open systems and to a method of computation which is practical and can be used where others cannot. We…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale…
Generalised Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion methods. A generalised Dyson boson-fermion mapping is a…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
The fermionic von Neumann entropy, the fermionic entanglement entropy and the fermionic relative entropy are defined for causal fermion systems. Our definition makes use of entropy formulas for quasi-free fermionic states in terms of the…
The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
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 paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…
It is commonly assumed that every quantum system is represented by some algebra of operators. Doubt is cast on this assumption by what appears, at first glance, to be a reasonable candidate for a quantum system that is not naturally…