Topology of QCD vacuum and color confinement

2002 ◽  
Vol 80 (7) ◽  
pp. 745-754 ◽  
Author(s):  
H C Chandola ◽  
H C Pandey ◽  
H Nandan
Keyword(s):  
Unit Length ◽  
Cylindrical Symmetry ◽  
Gauge Potential ◽  
Dynamical Structure ◽  
Field Equations ◽  
Abelian Gauge ◽  
Qcd Vacuum ◽  
Color Confinement ◽  
Restricted Form ◽  
Magnetic Symmetry

Using the magnetic symmetry structure of non-Abelian gauge theories of the Yang–Mills type, the mathematical foundation of dual chromodynamics in fiber-bundle form is discussed. The dual gauge potential in its restricted form is constructed in terms of magnetic vectors on global sections, which has been shown to lead the dual dynamics between topological charges and color isocharges. Constructing the Lagrangian for such dual theory, the dynamical breaking of magnetic symmetry by an effective potential is shown to push the QCD vacuum in a confining phase. The dynamical structure of the theory is investigated by deriving the field equations associated with the confining phase. The associated flux-tube structure responsible for the confinement is analyzed by computing the asymptotic string solutions of the field equations under cylindrical symmetry. Using the confining part of the dual restricted Lagrangian, the finite string energy per unit length is calculated and its implications on color confinement are discussed. PACS Nos.: 11.38Aw, 14.80Hv, 11.30Jw

DYONIC FLUX TUBE STRUCTURE OF NONPERTURBATIVE QCD VACUUM

2003 ◽  
Vol 18 (09) ◽  
pp. 1623-1635 ◽  
Author(s):  
H. C. CHANDOLA ◽  
H. C. PANDEY
Keyword(s):  
Flux Tube ◽  
Input Parameter ◽  
Gauge Potential ◽  
Field Equations ◽  
Pair Correlations ◽  
Qcd Vacuum ◽  
Nonperturbative Qcd ◽  
Magnetic Symmetry ◽  
Tube Structure ◽  
Dyonic Condensation

We study the flux tube structure of the nonperturbative QCD vacuum in terms of its dyonic excitations by using an infrared effective Lagrangian and show that the dyonic condensation of QCD vacuum has a close connection with the process of color confinement. Using the fiber bundle formulation of QCD, the magnetic symmetry condition is presented in a gauge covariant form and the gauge potential has been constructed in terms of the magnetic vectors on global sections. The dynamical breaking of the magnetic symmetry has been shown to lead the dyonic condensation of QCD vacuum in the infrared energy sector. Deriving the asymptotic solutions of the field equations in the dynamically broken phase, the dyonic flux tube structure of QCD vacuum is explored which has been shown to lead the confinement parameters in terms of the vector and scalar mass modes of the condensed vacuum. Evaluating the charge quantum numbers and energy associated with the dyonic flux tube solutions, the effect of electric excitation of monopole is analyzed using the Regge slope parameter (as an input parameter) and an enhancement in the dyonic pair correlations and the confining properties of QCD vacuum in its dyonically condensed mode has been demonstrated.

CRITICAL PARAMETERS OF PHASE TRANSITION IN DUAL QCD

2005 ◽  
Vol 20 (13) ◽  
pp. 2743-2752 ◽  
Author(s):  
H. C. CHANDOLA ◽  
DINESH YADAV ◽  
H. C. PANDEY ◽  
H. DEHNEN
Keyword(s):  
Phase Transition ◽  
Flux Tube ◽  
Intermediate Energy ◽  
Critical Parameters ◽  
Critical Flux ◽  
Flux Tubes ◽  
Qcd Vacuum ◽  
Color Confinement ◽  
Magnetic Symmetry ◽  
Dynamical Breaking

Color confinement is studied in dual version of SU (2) color gauge theory using its topological structure and the dynamical breaking of the magnetic symmetry which has been shown to effectively trigger the QCD monopole condensation in a dynamical way. The resulting flux tube structure of the QCD vacuum is explored which has been shown to lead to the perfect dual superconducting nature to the QCD vacuum in its dynamically broken phase. The analysis of the flux tube energy at different hadronic length scales has been shown to lead to the appearance of the strong confinement forces in QCD vacuum at large hadronic distances and an indication for the deconfinement phase at small scales. The analysis of the flux tube energy is then used to compute numerically the critical radius and the critical flux tube density of the phase transition from the flux tube phase to deconfined one inside hadrons. The numerical estimates are shown to be in fairly good agreement with the analytical values. The possible implications of these critical parameters on the formation of QGP as a result of the flux tubes fusion in intermediate energy regime are also discussed.

scholarly journals Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

2017 ◽  
Vol 2017 ◽  
pp. 1-26 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
Wave Function ◽  
Complex Number ◽  
Degrees Of Freedom ◽  
Unit Vector ◽  
Wave Functions ◽  
Field Equations ◽  
Abelian Gauge ◽  
Color Confinement ◽  
Complex Quaternion ◽  
Spatial Dimensions

The paper aims to apply the complex-sedenions to explore the wave functions and field equations of non-Abelian gauge fields, considering the spatial dimensions of a unit vector as the color degrees of freedom in the complex-quaternion wave functions, exploring the physical properties of the color confinement essentially. J. C. Maxwell was the first to employ the quaternions to study the electromagnetic fields. His method inspires subsequent scholars to introduce the quaternions, octonions, and sedenions to research the electromagnetic field, gravitational field, and nuclear field. The application of complex-sedenions is capable of depicting not only the field equations of classical mechanics, but also the field equations of quantum mechanics. The latter can be degenerated into the Dirac equation and Yang-Mills equation. In contrast to the complex-number wave function, the complex-quaternion wave function possesses three new degrees of freedom, that is, three color degrees of freedom. One complex-quaternion wave function is equivalent to three complex-number wave functions. It means that the three spatial dimensions of unit vector in the complex-quaternion wave function can be considered as the “three colors”; naturally the color confinement will be effective. In other words, in the complex-quaternion space, the “three colors” are only the spatial dimensions, rather than any property of physical substance.

scholarly journals An Effective Model for Glueballs and Dual Superconductivity at Finite Temperature

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Adamu Issifu ◽  
Francisco A. Brito
Keyword(s):  
Finite Temperature ◽  
Gluon Plasma ◽  
String Tension ◽  
Abelian Gauge ◽  
Confining Potential ◽  
Effective Masses ◽  
Qcd Vacuum ◽  
Color Confinement ◽  
Running Coupling ◽  
By Products

The glueballs lead to gluon and QCD monopole condensations as by-products of color confinement. A color dielectric function G ∣ ϕ ∣ coupled with a Abelian gauge field is properly defined to mediate the glueball interactions at confining regime after spontaneous symmetry breaking (SSB) of the gauge symmetry. The particles are expected to form through the quark-gluon plasma (QGP) hadronization phase where the free quarks and gluons start clamping together to form hadrons. The QCD-like vacuum η 2 m η 2 F μ ν F μ ν , confining potential V c r , string tension σ , penetration depth λ , superconducting and normal monopole densities ( n s   n n ), and the effective masses ( m η 2 and m A 2 ) will be investigated at finite temperature T . We also calculate the strong “running” coupling α s and subsequently the QCD β -function. The dual superconducting nature of the QCD vacuum will be investigated based on monopole condensation.

scholarly journals TOPOLOGICALLY MASSIVE GAUGE THEORY: A LORENTZIAN SOLUTION

2007 ◽  
Vol 22 (16n17) ◽  
pp. 2961-2976 ◽  
Author(s):  
K. SAYGILI
Keyword(s):  
Field Equation ◽  
Gauge Theory ◽  
Field Strength ◽  
Gauge Transformation ◽  
Global Section ◽  
Gauge Potential ◽  
Abelian Gauge ◽  
Abelian Field ◽  
Hopf Map ◽  
Topological Mass

We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space [Formula: see text] by means of an SU (1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map [Formula: see text] including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of [Formula: see text] as a trivial [Formula: see text] bundle over the upper portion of the pseudosphere [Formula: see text] which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto [Formula: see text] using a global section of the solution on [Formula: see text]. Then we discuss the integration of the field equation using the Archimedes map [Formula: see text]. We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on [Formula: see text].

scholarly journals Phase Change with Density Variation and Cylindrical Symmetry: Application to Selective Laser Melting

2019 ◽  
Vol 3 (3) ◽  
pp. 62 ◽  
Author(s):  
Fyrillas ◽  
Ioannou ◽  
Papadakis ◽  
Rebholz ◽  
Doumanidis
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Phase Change ◽  
Selective Laser Melting ◽  
Unit Length ◽  
Cylindrical Symmetry ◽  
Density Variation ◽  
Laser Melting ◽  
Molten Material ◽  
Melt Pool

In this paper we introduce an analytical approach for predicting the melting radius during powder melting in selective laser melting (SLM) with minimum computation duration. The purpose of this work is to evaluate the suggested analytical expression in determining the melt pool geometry for SLM processes, by considering heat transfer and phase change effects with density variation and cylindrical symmetry. This allows for rendering first findings of the melt pool numerical prediction during SLM using a quasi-real-time calculation, which will contribute significantly in the process design and control, especially when applying novel powders. We consider the heat transfer problem associated with a heat source of power Q' (W/m) per unit length, activated along the span of a semi-infinite fusible material. As soon as the line heat source is activated, melting commences along the line of the heat source and propagates cylindrically outwards. The temperature field is also cylindrically symmetric. At small times (i.e., neglecting gravity and Marangoni effects), when the density of the solid material is less than that of the molten material (i.e., in the case of metallic powders), an annulus is created of which the outer interface separates the molten material from the solid. In this work we include the effect of convection on the melting process, which is shown to be relatively important. We also justify that the assumption of constant but different properties between the two material phases (liquid and solid) does not introduce significant errors in the calculations. A more important result; however, is that, if we assume constant energy input per unit length, there is an optimum power of the heat source that would result to a maximum amount of molten material when the heat source is deactivated. The model described above can be suitably applied in the case of selective laser melting (SLM) when one considers the heat energy transferred to the metallic powder bed during scanning. Using a characteristic time and length for the process, we can model the energy transfer by the laser as a heat source per unit length. The model was applied in a set of five experimental data, and it was demonstrated that it has the potential to quantitatively describe the SLM process.

Renormalization Group and Color Confinement

1998 ◽  
Vol 12 (12n13) ◽  
pp. 1355-1364 ◽  
Author(s):  
K. Nishijima
Keyword(s):  
Renormalization Group ◽  
Gauge Symmetry ◽  
Quantum Chromodynamics ◽  
Asymptotic Freedom ◽  
Abelian Gauge ◽  
Color Confinement

It is shown that color confinement is an inevitable consequence of an unbroken non-Abelian gauge symmetry and the resulting asymptotic freedom of quantum chromodynamics.

THE GRAVITATIONAL FIELDS OF ELECTRIC AND MAGNETIC DIPOLES

1957 ◽  
Vol 35 (4) ◽  
pp. 477-482 ◽  
Author(s):  
Gerald E. Tauber
Keyword(s):  
Cylindrical Symmetry ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Magnetic Dipoles ◽  
Gravitational Fields ◽  
Einstein's Field Equations

Einstein's field equations are solved for cylindrical symmetry in the presence of electric and magnetic singularities (dipoles).

CURRENT CORRELATORS AND DUAL DESCRIPTION OF LONG DISTANCE QCD

2002 ◽  
Vol 17 (10) ◽  
pp. 599-607
Author(s):  
H. C. CHANDOLA ◽  
H. C. PANDEY
Keyword(s):  
Fibre Bundle ◽  
Dielectric Behavior ◽  
Strong Interactions ◽  
Macroscopic Description ◽  
Long Distance ◽  
Dielectric Parameters ◽  
Abelian Gauge ◽  
Microscopic Interactions ◽  
Magnetic Symmetry ◽  
Abelian Fields

An attempt has been made to analyze the magnetic symmetry of the non-Abelian gauge theory associated with the strong interactions using the fibre bundle formulation. Utilizing the gauge field topology, the analysis of dual dynamics associated with the non-Abelian fields is shown to have important bearings on the nonperturbative hadronic effects like confinement of colored quarks and gluons inside hadrons. The state of dual superconductivity for the magnetically condensed vacuum has been analyzed to understand the bulk QCD magnetic properties by evaluating the current correlators in magnetic gauge in terms of the dielectric parameters. The dielectric behavior has been shown to lead to the p-4 confining nature to the dual gluon propagators and to provide an effective macroscopic description of the complicated nonperturbative microscopic interactions of charged particles in dual QCD. The p-4 behavior of dual gluon propagator has also been shown to confirm the linearly rising inter-quark confining potential with an explicit dual gluon mass dependency in dual QCD.

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