Random center vortex model

2018 ◽  
Vol 33 (29) ◽  
pp. 1850170
Author(s):  
Derar Altarawneh
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Physical Space ◽  
Variable Number ◽  
Qualitative Properties ◽  
Yang Mills ◽  
Center Vortex ◽  
Vortex Density ◽  
Dimensional Space Time ◽  
Different Temperatures

This work presents a model of center vortices, expressed by random lines in three-dimensional space–time. Monte Carlo methods were used to ensemble these closed random lines. The physical space wherein the vortex lines are defined is a cuboid including periodic boundary conditions. Reconnections are allowed aside from moving, growing, and shrinking of the vortex configuration. Therefore, the ensemble contains a variable number of closed vortex clusters, which are considered significant in realizing the deconfining phase transition. The average vortex density and length are studied as a function of vortex density [Formula: see text] by using this model. At different temperatures, potential [Formula: see text] between quark and antiquark is studied as a function of distance [Formula: see text]. This model is able to emphasize the confinement physics qualitative properties in [Formula: see text] Yang–Mills theory.

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 Yang–Mills Theory of Gravity

Physics ◽  
2019 ◽  
Vol 1 (3) ◽  
pp. 339-359
Author(s):  
Malik Al Matwi
Keyword(s):  
Dimensional Space ◽  
Beta Function ◽  
Three Dimensional ◽  
Spin Current ◽  
Space Time ◽  
Yang Mills ◽  
Decomposition Space ◽  
Dimensional Space Time ◽  
Conserved Currents ◽  
Three Dimensional Space

The canonical formulation of general relativity (GR) is based on decomposition space–time manifold M into R × Σ , where R represents the time, and Ksi is the three-dimensional space-like surface. This decomposition has to preserve the invariance of GR, invariance under general coordinates, and local Lorentz transformations. These symmetries are associated with conserved currents that are coupled to gravity. These symmetries are studied on a three dimensional space-like hypersurface Σ embedded in a four-dimensional space–time manifold. This implies continuous symmetries and conserved currents by Noether’s theorem on that surface. We construct a three-form E i ∧ D A i (D represents covariant exterior derivative) in the phase space ( E i a , A a i ) on the surface Σ , and derive an equation of continuity on that surface, and search for canonical relations and a Lagrangian that correspond to the same equation of continuity according to the canonical field theory. We find that Σ i 0 a is a conjugate momentum of A a i and Σ i a b F a b i is its energy density. We show that there is conserved spin current that couples to A i , and show that we have to include the term F μ ν i F μ ν i in GR. Lagrangian, where F i = D A i , and A i is complex S O ( 3 ) connection. The term F μ ν i F μ ν i includes one variable, A i , similar to Yang–Mills gauge theory. Finally we couple the connection A i to a left-handed spinor field ψ , and find the corresponding beta function.

LOCALIZATION OF NONLOCAL LAGRANGIANS AND MASS GENERATION FOR NON-ABELIAN GAUGE FIELDS

2008 ◽  
Vol 23 (26) ◽  
pp. 4289-4313
Author(s):  
ALEXEY SEVOSTYANOV
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Fields ◽  
Green Functions ◽  
Coupling Constant ◽  
Mass Generation ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Three Dimensional Space

We introduce and study the four-dimensional analogue of a mass generation mechanism for non-Abelian gauge fields suggested in the paper, Phys. Lett. B403, 297 (1997), in the case of three-dimensional space–time. The construction of the corresponding quantized theory is based on the fact that some nonlocal actions may generate local expressions for Green functions. An example of such a theory is the ordinary Yang–Mills field where the contribution of the Faddeev–Popov determinant to the Green functions can be made local by introducing additional ghost fields. We show that the quantized Hamiltonian for our theory unitarily acts in a Hilbert space of states and prove that the theory is renormalizable to all orders of perturbation theory. One-loop coupling constant and mass renormalizations are also calculated.

Dynamics of a composite system in a point source-induced space–time

2021 ◽  
pp. 2150144
Author(s):  
Abdullah Guvendi
Keyword(s):  
Point Source ◽  
Composite System ◽  
Dimensional Space ◽  
Energy Levels ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Space Time ◽  
Spin Coupling ◽  
Quantum Oscillator ◽  
Dimensional Space Time

We investigate the dynamics of a composite system ([Formula: see text]) consisting of an interacting fermion–antifermion pair in the three-dimensional space–time background generated by a static point source. By considering the interaction between the particles as Dirac oscillator coupling, we analyze the effects of space–time topology on the energy of such a [Formula: see text]. To achieve this, we solve the corresponding form of a two-body Dirac equation (fully-covariant) by assuming the center-of-mass of the particles is at rest and locates at the origin of the spatial geometry. Under this assumption, we arrive at a nonperturbative energy spectrum for the system in question. This spectrum includes spin coupling and depends on the angular deficit parameter [Formula: see text] of the geometric background. This provides a suitable basis to determine the effects of the geometric background on the energy of the [Formula: see text] under consideration. Our results show that such a [Formula: see text] behaves like a single quantum oscillator. Then, we analyze the alterations in the energy levels and discuss the limits of the obtained results. We show that the effects of the geometric background on each energy level are not same and there can be degeneracy in the energy levels for small values of the [Formula: see text].

QUANTUM COMPUTING WITH NON-ABELIAN QUASIPARTICLES

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1372-1378 ◽  
Author(s):  
N. E. BONESTEEL ◽  
L. HORMOZI ◽  
G. ZIKOS ◽  
S. H. SIMON
Keyword(s):  
Dimensional Space ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Operations ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
Two Space Dimensions ◽  
Topological Quantum Computation

In topological quantum computation quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum operations are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum operations depend only on the topology of the braids formed by these world-lines. We describe recent work showing how to find braids which can be used to perform arbitrary quantum computations using a specific kind of quasiparticle (those described by the so-called Fibonacci anyon model) which are thought to exist in the experimentally observed ν = 12/5 fractional quantum Hall state.

scholarly journals About renormalized effective action for the Yang-Mills theory in four-dimensional space-time

2018 ◽  
Vol 191 ◽  
pp. 06001
Author(s):  
A.V. Ivanov
Keyword(s):  
Infinite Series ◽  
Effective Action ◽  
Dimensional Space ◽  
Space Time ◽  
Coupling Constant ◽  
Asymptotic Approach ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Bare Coupling Constant ◽  
Renormalization Theory

This work is related to the asymptotic approach in the renormalization theory and its problems. As the main example, the Yang-Mills theory in four-dimensional space-time is considered. It has been shown earlier [16] that using the asymptotic of the bare coupling constant one can find an expression for the renormalized effective action, however, this formula has problems (divergence ln " and infinite series). This work shows the relation of these values and provides an answer for the renormalized effective action.

scholarly journals Concept of the time in language and text (contextual time markers)

2021 ◽  
Vol 14 (1(14)/2020) ◽  
pp. 143-149
Author(s):  
Natalia Grushina
Keyword(s):  
Foreign Language ◽  
Cognitive Linguistics ◽  
Dimensional Space ◽  
Human Life ◽  
Three Dimensional ◽  
Cognitive Approach ◽  
The Social ◽  
Russian Literary ◽  
Dimensional Space Time ◽  
Perception Of Time

The aim of this paper is to study different time representations in language and text. Time is an abstract category firmly connected to human life, it can be considered to be the fourth dimension of reality, used to describe events in three-dimensional space. Time has been studied from different points of view and in different aspects. The perception of time can vary depending on the social and cultural environment. That is why it is so important to pay special attention to a variety of time representations when studying a foreign language. In this article I consider different time markers represented in language (English and Russian) and contextual time markers we can find in texts for reading comprehension activities at advanced levels when studying Russian as a foreign language. I compare language and contextual time markers using a cognitive approach to text units. As an example, I take time markers from the texts published in a popular Russian literary magazine Novy mir at the turn of the 21 century. Novy mir is a very famous in Russia for its liberal position and history within the dissident movement during Soviet epoch Keywords: concept of time, time markers, text and discourse, cognitive linguistics

scholarly journals Lorentz-violating effects in three-dimensional QED

2014 ◽  
Vol 29 (22) ◽  
pp. 1450112 ◽  
Author(s):  
R. Bufalo
Keyword(s):  
Quantum Electrodynamics ◽  
Lagrangian Density ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Nonminimal Coupling ◽  
Coupling Term ◽  
Interaction Terms ◽  
Higher Derivative ◽  
Dimensional Space Time

Inspired in discussions presented lately regarding Lorentz-violating interaction terms in B. Charneski, M. Gomes, R. V. Maluf and A. J. da Silva, Phys. Rev. D86, 045003 (2012); R. Casana, M. M. Ferreira Jr., R. V. Maluf and F. E. P. dos Santos, Phys. Lett. B726, 815 (2013); R. Casana, M. M. Ferreira Jr., E. Passos, F. E. P. dos Santos and E. O. Silva, Phys. Rev. D87, 047701 (2013), we propose here a slightly different version for the coupling term. We will consider a modified quantum electrodynamics with violation of Lorentz symmetry defined in a (2+1)-dimensional space–time. We define the Lagrangian density with a Lorentz-violating interaction, where the space–time dimensionality is explicitly taken into account in its definition. The work encompasses an analysis of this model at both zero and finite-temperature, where very interesting features are known to occur due to the space–time dimensionality. With that in mind, we expect that the space–time dimensionality may provide new insights about the radiative generation of higher-derivative terms into the action, implying in a new Lorentz-violating electrodynamics, as well the nonminimal coupling may provide interesting implications on the thermodynamical quantities.

scholarly journals SPIN GAUGE THEORY OF GRAVITY IN CLIFFORD SPACE: A REALIZATION OF KALUZA–KLEIN THEORY IN FOUR-DIMENSIONAL SPACE–TIME

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5905-5956 ◽  
Author(s):  
MATEJ PAVŠIČ
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Dirac Field ◽  
Spin Connection ◽  
Yang Mills ◽  
Object A ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
The Right ◽  
Kaluza Klein

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U (1) × SU (2) × SU (3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.

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