scholarly journals On the representation theory of the Bondi–Metzner–Sachs group and its variants in three space–time dimensions

2017 ◽  
Vol 58 (7) ◽  
pp. 071705 ◽  
Author(s):  
Evangelos Melas
Keyword(s):  
Representation Theory ◽  
Space Time ◽  
Three Space

Theory of the Stationary Self-Consistent Universe

2021 ◽  
Author(s):  
Alexander Shamailovich Avshalumov
Keyword(s):  
Quantum Physics ◽  
Space Time ◽  
Theoretical Physics ◽  
Time Model ◽  
Zero Curvature ◽  
Modern Cosmology ◽  
Simultaneous Existence ◽  
Three Space ◽  
Space Time Model ◽  
The Universe

Since the creation of GR and subsequent works in cosmology, the question of the curvature of space in the Universe is considered one of the most important and debated to this day. This is evident, because the curvature of space depends whether the Universe expands, contracts or is static. These discussions allowed the author to propose a paradoxical idea: simultaneous existence in the Universe of three interconnected space-times (positive, negative and zero curvature) and on this basis, to develop a theory in which each space-time plays its own role and develops in a strict accordance with its sign of curvature. The three space-time model of the structure of the Universe, proposed by the author, allows to solve many fundamental problems of modern cosmology and theoretical physics and creates the basis for building a unified physical theory (including one that unites GR and quantum physics).

Relativistic bound states in three space-time dimensions in Minkowski space

2016 ◽  
Author(s):  
C. Gutierrez ◽  
V. Gigante ◽  
T. Frederico ◽  
Lauro Tomio
Keyword(s):  
Minkowski Space ◽  
Bound States ◽  
Space Time ◽  
Relativistic Bound States ◽  
Three Space

scholarly journals Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra

2019 ◽  
Vol 798 ◽  
pp. 135005 ◽  
Author(s):  
Diego M. Peñafiel ◽  
Patricio Salgado-Rebolledo
Keyword(s):  
Space Time ◽  
Three Space

Collision and rotation of solitons in three space-time dimensions

1981 ◽  
Vol 101 (3) ◽  
pp. 204-208 ◽  
Author(s):  
J.K. Drohm ◽  
L.P. Kok ◽  
Yu.A. Simonov ◽  
J.A. Tjon ◽  
A.I. Veselov
Keyword(s):  
Space Time ◽  
Three Space

CHRONOMETRIC INVARIANCE AND STRING THEORY

2008 ◽  
Vol 23 (11) ◽  
pp. 797-813 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Physical Space ◽  
Space Time ◽  
Kerr Metric ◽  
De Sitter ◽  
Superstring Theory ◽  
Dimensional Space Time ◽  
Raychaudhuri Equations ◽  
Three Space

The Einstein–Hilbert Lagrangian R is expressed in terms of the chronometrically invariant quantities introduced by Zel'manov for an arbitrary four-dimensional metric gij. The chronometrically invariant three-space is the physical space γαβ = -gαβ+e2ϕ γαγβ, where e 2ϕ = g00 and γα = g0α/g00, and whose determinant is h. The momentum canonically conjugate to γαβ is [Formula: see text], where [Formula: see text] and ∂t≡ e -ϕ∂0 is the chronometrically invariant derivative with respect to time. The Wheeler–DeWitt equation for the wave function Ψ is derived. For a stationary space-time, such as the Kerr metric, παβ vanishes, implying that there is then no dynamics. The most symmetric, chronometrically-invariant space, obtained after setting ϕ = γα = 0, is [Formula: see text], where δαβ is constant and has curvature k. From the Friedmann and Raychaudhuri equations, we find that λ is constant only if k=1 and the source is a perfect fluid of energy-density ρ and pressure p=(γ-1)ρ, with adiabatic index γ=2/3, which is the value for a random ensemble of strings, thus yielding a three-dimensional de Sitter space embedded in four-dimensional space-time. Furthermore, Ψ is only invariant under the time-reversal operator [Formula: see text] if γ=2/(2n-1), where n is a positive integer, the first two values n=1,2 defining the high-temperature and low-temperature limits ρ ~ T±2, respectively, of the heterotic superstring theory, which are thus dual to one another in the sense T↔1/2π2α′T.

scholarly journals DIFFERENTIAL CALCULUS AND CONNECTIONS ON A QUANTUM PLANE AT A CUBIC ROOT OF UNITY

2000 ◽  
Vol 12 (02) ◽  
pp. 227-285 ◽  
Author(s):  
R. COQUEREAUX ◽  
A. O. GARCÍA ◽  
R. TRINCHERO
Keyword(s):  
Representation Theory ◽  
Quantum Group ◽  
Lorentz Group ◽  
Differential Calculus ◽  
Differential Algebra ◽  
Space Time ◽  
Quantum Plane ◽  
Root Of Unity ◽  
Finite Dimensional

We consider the algebra of N×N matrices as a reduced quantum plane on which a finite-dimensional quantum group ℋ acts. This quantum group is a quotient of [Formula: see text], q being an Nth root of unity. Most of the time we shall take N=3; in that case dim(ℋ)=27. We recall the properties of this action and introduce a differential calculus for this algebra: it is a quotient of the Wess–Zumino complex. The quantum group ℋ also acts on the corresponding differential algebra and we study its decomposition in terms of the representation theory of ℋ. We also investigate the properties of connections, in the sense of non commutative geometry, that are taken as 1-forms belonging to this differential algebra. By tensoring this differential calculus with usual forms over space-time, one can construct generalized connections with covariance properties with respect to the usual Lorentz group and with respect to a finite-dimensional quantum group.

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