Related papers: Matter in Discrete Space-Times

We provide a detailed decomposition of Wigner's particles, defined as unitary irreducible representations of the Poincar\'e group, in terms of unitary representations of its Lorentz subgroup. As pointed out before us, this decomposition…

We write down an explicit projection that maps any given 4-spinor to a point in 3+1 spacetime while commuting with the Lorentz action. This suggests that a Lorentz invariant theory - including spacetime itself - has a more natural…

Time crystals are exotic phases of matter characterized by a broken time-translational symmetry, such that the ground state of the system evolves in time in a periodic fashion. Even though the time-crystal concept was introduced relatively…

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…

The internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The $O(3)$-like little group for a massive particle at rest and the $E(2)$-like little group of a massless particle are two different…

The classical motion of spinning particles can be described without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincare' group;…

In cosmology it has become usual to introduce new entities as dark matter and dark energy in order to explain otherwise unexplained observational facts. Here, we propose a different approach treating spacetime as a continuum endowed with…

In this paper, we consider the Poincare group (space time). In mathematics, the Poincar\'e group of spacetime, named after Henri Poincar\'e, is the group of isometries of Minkowski spacetime, introduced by Hermann Minkowski. It is a…

Although we lack complete understanding of quantum aspects of gravitation, it is usually agreed, using general arguments, that a final quantum gravity theory will endow space and time with some (fundamental or effective) notion of…

Solutions of the sourceless Einstein's equation with weak and strong cosmological constants are discussed by using In\"on\"u-Wigner contractions of the de Sitter groups and spaces. The more usual case corresponds to a weak…

We analyze the spectrum of time observable in noncommutative cosmological model introduced in [5], defined by $(\rho, s=\frac 12)\,$ representation of the de Sitter group. We find that time has peculiar property: it is not self-adjoint, but…

We prove that every continuous map acting on the four-dimensional Minkowski space and preserving light cones in one direction only is either a Poincar\'e similarity, that is, a product of a Lorentz transformation and a dilation, or it is of…

The theory of defects in ordered and ill-ordered media is a well-advanced part of condensed matter physics. Concepts developed in this field also occur in the study of spacetime singularities, namely: i)- the topological theory of quantized…

This study looks at motion of particles using mathematical methods of chronometric invariants (physical observable values in General Relativity). It is shown that aside for mass-bearing particles and light-like particles "zero-particles"…

In this work, we show that extending the standard description of space-time symmetries from groups of isometries to the more flexible framework of kinematical groupoids allows for the extension of Wigner's program to curved space-times. We…

Inspired by previous work in 2+1 dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and…

We show that the exact solution of the two_superbody problem in N=2 Chern Simons Supergravity in 2+1 dimensions leads to a supermultiplet of space-times. This supersymmetric space-time is characterized by the two gauge invariant observables…

It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…

We continue the program, presented in previous Symposia, of discretizing physical models. In particular we calculate the integral Lorentz transformations with the help of discrete reflection groups, and use them for the covariance of…

Quantum theory and relativity are the pillar theories on which our understanding of physics is based. Poincar\'e invariance is a fundamental physical principle stating that the experimental results must be the same in all inertial reference…