Related papers: Fermion Systems in Discrete Space-Time Exemplifyin…

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under…

A systematic procedure is developed for constructing fermion systems in discrete space-time which have a given outer symmetry. The construction is illustrated by simple examples. For the symmetric group, we derive constraints for the number…

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…

The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is…

In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a…

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…

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…

We put forward a model of discrete physical space that can account for the structure of space- time, give an interpretation to the postulates of quantum mechanics and provide a possible explanation to the organization of the standard model…

We compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. We find that octonions and, more generally, tensor products of…

Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or…

Where did elementary particles come from? What mechanisms are responsible for their occurrence and maintenance? Are they compound or truly elementary? Is vacuum primordial soup where elementary particles are born? Are quantum behavior and…

We give a brief introduction to causal fermion systems with a focus on the geometric structures in space-time.

In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…

There are several indications (from different approaches) that Spacetime at the Plank Scale could be discrete. One approach to Quantum Gravity that takes this most seriously is the Causal Sets Approach. In this approach spacetime is…

We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension,…

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…

Discrete time-crystals are periodically driven quantum many-body systems with broken discrete-time translational symmetry, a non-equilibrium steady state representing self-organization of motion of quantum particles. Observations of…

Time crystals are a phase of matter, for which the discrete time symmetry of the driving Hamiltonian is spontaneously broken. The breaking of discrete time symmetry has been observed in several experiments in driven spin systems. Here, we…

The experiments conducted by various scientific groups indicate that, in dense two-dimensional systems of elongated particles subjected to vibration, the pattern formation is possible. Computer simulations have evidenced that the random…

We have calculated the ground state wave functions for a systems of multicomponent interacting fermions. We show that it describes the state with spontaneously broken chiral symmetry. In the limit of an infinitely strong interaction it…