Related papers: From Discrete Space-Time to Minkowski Space: Basic…
In this work the spontaneous symmetry breaking in certain nonlinear theories with second-class constraints is explored. Using the Dirac's method we perform an analysis of the constraints and the counting of the degrees of freedom. The…
Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Many quantum lattice models have an emergent relativistic description in their continuum limit. The celebrated example is graphene, whose continuum limit is described by the Dirac equation on a Minkowski spacetime. Not only does the…
We extend a recently developed "tangent fermion" method to discretize the Hamiltonian of a helical Luttinger liquid on a one-dimensional lattice, including two-particle backscattering processes that may open a gap in the spectrum. The…
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…
"What is the difference between space and time?" is an ancient question that remains a matter of intense debate. In Newtonian mechanics time is absolute, while in Einstein's theory of relativity time and space combine into Minkowski…
In this paper, we present a new theoretical scenario in which both dynamical Dirac fermions and Einstein's gravity with a positive cosmological constant and torsion emerge via a spontaneous symmetry breaking in a topological phase. This…
Dilatation, i.e. scale, symmetry in the presence of the dilaton in Minkowski space is derived from diffeomorphism symmetry in curved spacetime, incorporating the volume-preserving diffeomorphisms. The conditions for scale invariance are…
This article expands for spinor fields the recently developed Dynamical Bridge formalism which relates a linear dynamics in a curved space to a nonlinear dynamics in Minkowski space. Astonishingly, this leads to a new geometrical mechanism…
The linearized field equations for causal fermion systems in Minkowski space are analyzed systematically using methods of functional analysis and Fourier analysis. Taking into account a direction-dependent local phase freedom, we find a…
The causal set program as well as the Wolfram physics project leave open the problem of how a graph that is a (3+1)-dimensional Minkowski-spacetime according to its simple geodesic distances, could be generated solely from simple…
A non-canonical correspondence of the complete sets of solutions to the Dirac and Klein-Gordon free equations in Minkowski space-time is established. This allows for a novel viewpoint on the relationship of relativistic equations for…
We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime, focusing on a (1+1)-dimensional case in which the evolution of the scale factor is set by the equations of…
For causal graphs we propose a definition of proper time which for small scales is based on the concept of volume, while for large scales the usual definition of length is applied. The scale where the change from "volume" to "length" occurs…
We consider introducing the Dirac sea in a quantum cellular automata model of fermions in discrete spacetime which approximates the Dirac equation in the continuum limit. However, if we attempt to fill up the `negative' energy states, we…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
Kinematical and dynamical mechanisms leading to the spontaneous breaking of space-time symmetries are described. The symmetries affected are space and time translations, space rotations, scale and conformal transformations. Applications are…
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…