Related papers: Causal Fermion Systems: A Primer for Lorentzian Ge…
A simplified Walecka-type model is investigated in a cosmological scenario. The model includes fermionic, scalar and vector fields as sources. It is shown that their interactions, taking place in a Robertson-Walker metric, could be…
We present a framework for the dynamics of causal sets and coupled matter fields, which is a simplification and generalization of an approach we recently proposed. Given a set of fields including the gravitational one, the main step in…
The scientific rigor and computational methods of causal inference have had great impacts on many disciplines, but have only recently begun to take hold in spatial applications. Spatial casual inference poses analytic challenges due to…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
We consider two type of systems, a linear singular discrete time system and a linear singular fractional discrete time system whose coefficients are square constant matrices. By assuming that the input vector changes only at equally space…
We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.
Based on the recent work \cite{PII} we put forward a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations,…
This paper presents a novel and systematic formalism for deriving classical field equations within the framework ofcausal fermion systems, explicitly accounting for higher-order corrections such as quantum effects and those arising from…
We discuss the problem of determining the spacetime structure. We show that when we are using only topological methods the spacetime can be modelled as an R- or Q-compact space although the R-compact spaces seem to be more appropriate.…
We investigate the compatibility of Lorentzian amalgamation with various properties of Lorentzian pre-length spaces. In particular, we give conditions under which gluing of Lorentzian length spaces yields again a Lorentzian length space and…
In order to construct a quantum theory of gravity, we may have to abandon certain assumptions we were making. In particular, the concept of spacetime as a continuum substratum is questioned. Causal Sets is an attempt to construct a quantum…
Lorentzian frames may belong to one of the 199 causal classes. Of these numerous causal classes, people are essentially aware only of two of them. Nevertheless, other causal classes are present in some well-known solutions, or present a…
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…
We propose the quantum mechanical description of complex systems should be performed using two types of causality relation: the ordering relation ($x\prec y$) and the subset relation ($A\subseteq B$). The structures with two ordering…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
We study discrete Lorentzian spectral geometry by investigating to what extent causal sets can be identified through a set of geometric invariants such as spectra. We build on previous work where it was shown that the spectra of certain…
The paper discusses the following topics: spinor coverings for the full Lorentz group, intrinsic parity of fermions, Majorana fermions, spinor structure of space models, two types of spacial spinors, parametrization of spinor spaces by…
At present we have only the very successful but phenomenological Einstein geometrical modelling of the spacetime phenomenon. This geometrical model provides a `container' for other theories, in particular the quantum field theories. Here we…