scholarly journals QCD Theory of the Hadrons and Filling the Yang–Mills Mass Gap

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1887
Author(s):  
Jay R. Yablon
Keyword(s):  
Magnetic Monopoles ◽  
Exclusion Principle ◽  
Color Singlet ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Mass Gap ◽  
Net Flux ◽  
Strength Gradient ◽  
Electric Source ◽  
The Magnetic Field

The rank-3 antisymmetric tensors which are the magnetic monopoles of SU(N) Yang–Mills gauge theory dynamics, unlike their counterparts in Maxwell’s U(1) electrodynamics, are non-vanishing, and do permit a net flux of Yang–Mills analogs to the magnetic field through closed spatial surfaces. When electric source currents of the same Yang–Mills dynamics are inverted and their fermions inserted into these Yang–Mills monopoles to create a system, this system in its unperturbed state contains exactly three fermions due to the monopole rank-3 and its three additive field strength gradient terms in covariant form. So to ensure that every fermion in this system occupies an exclusive quantum state, the Exclusion Principle is used to place each of the three fermions into the fundamental representation of the simple gauge group with an SU(3) symmetry. After the symmetry of the monopole is broken to make this system indivisible, the gauge bosons inside the monopole become massless, the SU(3) color symmetry of the fermions becomes exact, and a propagator is established for each fermion. The monopoles then have the same antisymmetric color singlet wavefunction as a baryon, and the field quanta of the magnetic fields fluxing through the monopole surface have the same symmetric color singlet wavefunction as a meson. Consequently, we are able to identify these fermions with colored quarks, the gauge bosons with gluons, the magnetic monopoles with baryons, and the fluxing entities with mesons, while establishing that the quarks and gluons remain confined and identifying the symmetry breaking with hadronization. Analytic tools developed along the way are then used to fill the Yang–Mills mass gap.

scholarly journals QCD theory of the hadrons and filling the Yang-Mills mass gap

2020 ◽  
Author(s):  
Jay R. Yablon
Keyword(s):  
Magnetic Monopoles ◽  
Exclusion Principle ◽  
Color Singlet ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Mass Gap ◽  
Net Flux ◽  
Strength Gradient ◽  
Electric Source ◽  
The Magnetic Field

The rank-3 antisymmetric tensors which are the magnetic monopoles of SU(N) Yang-Mills gauge theory dynamics, unlike their counterparts in Maxwell’s U(1) electrodynamics, are non-vanishing, and do permit a net flux of Yang-Mills analogs to the magnetic field through closed spatial surfaces. When electric source currents of the same Yang-Mills dynamics are inverted and their fermions inserted into these Yang-Mills monopoles to create a system, this system in its unperturbed state contains exactly 3 fermions due to the monopole rank-3 and its 3 additive field strength gradient terms in covariant form. So to ensure that every fermion in this system occupies an exclusive quantum state, the Exclusion Principle is used to place each of the 3 fermions into the fundamental representation of the simple gauge group with an SU(3) symmetry. After the symmetry of the monopole is broken to make this system indivisible, the gauge bosons inside the monopole become massless, the SU(3) color symmetry of the fermions becomes exact, and a propagator is established for each fermion. The monopoles then have the same antisymmetric color singlet wavefunction as a baryon, and the field quanta of the magnetic fields fluxing through the monopole surface have the same symmetric color singlet wavefunction as a meson. Consequently, we are able to identify these fermions with colored quarks, the gauge bosons with gluons, the magnetic monopoles with baryons, and the fluxing entities with mesons, while establishing that the quarks and gluons remain confined and identifying the symmetry breaking with hadronization. Analytic tools developed along the way are then used to fill the Yang-Mills mass gap.

Existence of magnetic monopoles in higher dimensions is analogous to unipolar gravity

2020 ◽  
Author(s):  
Deep Bhattacharjee
Keyword(s):  
Flux Density ◽  
Higher Dimensions ◽  
Closed Surface ◽  
Magnetic Monopoles ◽  
Surface Integral ◽  
Flux Tubes ◽  
Spatial Dimensions ◽  
Net Flux ◽  
Field Lines ◽  
The Universe

Gravity has been leaking in higher dimensions in the bulk. Gravity being a closed string is not attached or does not have any endpoints unlike photons to any Dirichlet (p)-Branes and therefore can travel inter-dimensional without any hindrance. In LHC, CERN, Gravitons are difficult to detect as they last for such a short span of time and in most of the cases invisible as because they can escape to higher spatial dimensions to the maximum of 10, as per 'M'-Theory. Gravity being one of the 4-Fundamental forces is weaker than all 3 (strong and weak nuclear force, electromagnetism) and therefore a famous problem has been made in particle physics called the 'hierarchy problem'. Through comprehensive analysis and research I have come to the conclusion that if dimension is 5 (or 4 if we neglect the temporal dimensions) then an old approach is there for the compactification of the dimensions as per Kaluza-Klein theory and the most important implications of this theory is that an unification of electromagnetism with gravitation occurs in the fifth dimensions, therefore we can conclude that both the charge (electric as well as magnetic and gravity) are dependent of each other in case of Dimensions greater than 4 (5 if time is added). Now, basic principles of electromagnetic theory states that the field-flux density through a closed surface like a T 2 Torus when integrated over the surface area leads to a zero flux. That means there is no flux outside this closed surface integral. However, if the surface is open then the field flux density is not zero and this preserves the concept of magnetic monopoles. However, in a paper in 1931,[1] Dirac approaches monopole theory of magnetism through a different perspectives that, if all the electrical charges of the universe is quantized[2] then there is a suitable (not yet proved though) existence of monopoles; however this are not well understood as of today's scenario. In condensed matter physics, plasma physics and magneto hydrodynamics, there are flux tubes and as the both ends of the flux tubes are independent of each other then the net flux through the cylinder is zero as the amount of field lines entering the tube on one side is equal to the amount of field lines exit from the other end. And in the sides of the cylinder or the flux tube there is no escape of field lines, hence, net flux is conserved. There also exists a type of 'Quasiparticles' that can act as a monopole.[3][4][5] Now, from the perspectives of the Guess law of electromagnetism, if there exists a magnetic monopole then the net charge or flux density over a surface is not zero rather the divergence of the flux density B is 4 [6]and an alternative approach of the 'monopole' can be achieved by increasing the spatial dimensions by a factor of 1 or more. The Gravity has no such poles and therefore can be considered as a unipolar flux density existing throughout the universe and is applicable to the inverse square law of decreasing magnitude via distance as 1/r 2. However, a magnet is always of bipolar with a north and South Pole. If a magnet can be broken then also the broken parts develop the other poles and become bipolar. However, there are tiny domains inside a magnet and if a magnet can be heated to approx. 700℃ then all the poles disappeared and if its cooled quickly, rather very quickly then the tiny domains inside the magnet would not get enough time to rearrange themselves and multipolar magnet is developed therefore to preserve the bipolar properties, the magnet should be cooled slowly allowing the time given to the tiny domains top rearrange themselves. Therefore, even multipole can be achieved quite easily but not the monopoles. So, the equation for a closed surface integral of a flux density without monopole is ∯(S) B dS = 0 or ∇ • B = 0 and that closed surface can be considered as 2 types namely (we will discuss about torus) as because in string theory compactification of higher spatial dimensions occurs in torus.

FINITE ENERGY ONE-HALF MONOPOLE SOLUTIONS

2012 ◽  
Vol 27 (40) ◽  
pp. 1250233 ◽  
Author(s):  
ROSY TEH ◽  
BAN-LOONG NG ◽  
KHAI-MING WONG
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Topological Charge ◽  
Magnetic Monopole ◽  
Magnetic Charge ◽  
Finite Energy ◽  
Spatial Infinity ◽  
Yang Mills ◽  
The Magnetic Field

We present finite energy SU(2) Yang–Mills–Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole at the origin and a semi-infinite Dirac string on one-half of the z-axis carrying a magnetic flux of [Formula: see text] going into the origin. Hence the net magnetic charge is zero. The gauge potentials are singular along one-half of the z-axis, elsewhere they are regular.

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

scholarly journals Possible Explanation of the Quark Confinement and Asymptotic Freedom, and Possible Solution to the Yang-Mills Mass Gap Problem

2019 ◽  
Vol 16 (1) ◽  
pp. 391-478
Author(s):  
Antonio Puccini
Keyword(s):  
Gauge Theories ◽  
Rest Mass ◽  
Mathematical Structure ◽  
Physical Reality ◽  
Asymptotic Freedom ◽  
Nuclear Forces ◽  
Spatial Confinement ◽  
Yang Mills ◽  
Mass Gap ◽  
Narrow Space

With this work, we try to answer 3 fundamental questions that have plagued mathematicians and physicists for several decades. As known, the spontaneous symmetry breaking (SSB) and the Brout-Englert-Higgs Mechanism (BEH-M) solved the Yang-Mills Mass Gap Problem. However, various mathematicians, even prestigious ones, consider the basic assumptions of the gauge theories to be wrong, as well as in conflict with the experimental evidences and in clear disagreement with the facts, distorcing the physical reality itself. Likewise, the Quantum Fields Theory (QFT) is mathematically inconsistent, adopting a mathematical structure somewhat complicated and arbitrary, which does not satisfy the strong demands for coherence. The weakest point of the gauge theories, in our opinion, consists in imposing that all the particles must be free of an intrinsic mass (massless). On the contrary, even for the particle considered universally massless, i.e. the photon (P), our calculations show a dynamic-mass, a push-momentum (p) of 1.325⋅10−22[g⋅cm/s]. That is, an optic P hits a particle with an energy-mass greater than 100 protons rest-mass’. It is clear that if we replaced this value with the full value of the P inserted in the equations of the Perturbation Theory, QFT and Yang-Mills theories, all divergences, that is all zeroes and infinities, would suddenly disappear. Consequently, the limits imposed by the SSB disappear so that there is no longer any need to deny the mass to the Nuclear Forces bosons, including the Yang-Mills b quantum. Still, the photons (Ps) are the basis of the quantum vacuum energy, which is distributed ubiquitously, also within the intra-atomic spaces. It is likely that a lot of Ps were trapped in atomic nuclei (at the time of nucleosynthesis) and among quarks (Qs) at the time of primordial nucleonic synthesis. We believe that when Qs get too close to each other, till repelling each other (Asymptotic Freedom of Qs), this may depend on the presence of a multitude of Ps that, no further compressible, begin to exert an antigravity repulsive force, just as a Dark Energy. This limit to Compressibility (C) of the radiation is shown in equation: PV 4/3 = C, where V is the volume, and P is the Pressure of the photonic gas. Quantum Mechanics plays a crucial role, through the Uncertainty Principle, in the spatial Confinement of Qs, which have remained eternally confined in an extremely narrow space by the  Strong Interaction, but in primis by the very short range (likely ≈8.44[±1.44]⋅10-16cm) and lifetime of gluon(G) which, from our calculations, is ≈2.73[±0.564]⋅10-26 sec. Therefore, a new parameter may be added to the Qs and G spatial Confinement: the b quantum or G Temporal Confinement (and of their Colours and anti-Colours). 

scholarly journals Generalization of the Yang–Mills theory

2016 ◽  
Vol 31 (01) ◽  
pp. 1630003 ◽  
Author(s):  
G. Savvidy
Keyword(s):  
Beta Function ◽  
Coupling Constants ◽  
Standard Theory ◽  
Large Integer ◽  
Tree Level ◽  
Gauge Fields ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Conformally Invariant ◽  
Vector Gauge

We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincaré algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan–Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that it is leading to the theory which is conformally invariant at very high energies. The proposed extension may lead to a natural inclusion of the standard theory of fundamental forces into a larger theory in which vector gauge bosons, leptons and quarks represent a low-spin subgroup. We consider a possibility that inside the proton and, more generally, inside hadrons there are additional partons — tensorgluons, which can carry a part of the proton momentum. The extension of QCD influences the unification scale at which the coupling constants of the Standard Model merge, shifting its value to lower energies.

scholarly journals The World as Quarks, Leptons and Bosons

1976 ◽  
Vol 29 (6) ◽  
pp. 347 ◽  
Author(s):  
M Gell-Mann
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Strong Interactions ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Electromagnetic Interactions ◽  
The World

A descriptive review is given of gauge theories of weak, electromagnetic and strong interactions. The strong interactions are interpreted in terms of an unbroken Yang-Mills gauge theory based on SU(3) colour symmetry of quarks and gluons. The confinement mechanism of quarks, gluons and other nonsinglets is discussed. The unification of the weak and electromagnetic interactions through a broken Yang-Mills gauge theory is described. In total the basic constituents are then the quarks, leptons and gauge bosons.

scholarly journals Magnetic monopoles in pure $SU (2)$ Yang–Mills theory with a gauge-invariant mass

2018 ◽  
Vol 2018 (10) ◽  
Author(s):  
Shogo Nishino ◽  
Ryutaro Matsudo ◽  
Matthias Warschinke ◽  
Kei-Ichi Kondo
Keyword(s):  
Invariant Mass ◽  
Magnetic Monopoles ◽  
Gauge Invariant ◽  
Yang Mills

scholarly journals Black holes in magnetic monopoles with a dark halo

2019 ◽  
Vol 34 (01) ◽  
pp. 1950002 ◽  
Author(s):  
A. Lugo ◽  
J. M. Pérez Ipiña ◽  
F. A. Schaposnik
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Scalar Potential ◽  
Magnetic Monopoles ◽  
Dark Halo ◽  
Higgs Potential ◽  
Coupling Constant ◽  
Horizon Radius ◽  
Yang Mills ◽  
Higgs Portal

We study a spontaneously broken Einstein–Yang–Mills–Higgs model coupled via a Higgs portal to an uncharged scalar [Formula: see text]. We present a phase diagram of self-gravitating solutions showing that depending on the choice of parameters of the [Formula: see text] scalar potential and the Higgs portal coupling constant [Formula: see text], one can identify different regions: If [Formula: see text] is sufficiently small, a [Formula: see text] halo is created around the monopole core which in turn surrounds a black hole. For larger values of [Formula: see text], no halo exists and the solution is just a black hole monopole one. When the horizon radius grows and becomes larger than the monopole radius, solely a black hole solution exists. Because of the presence of the [Formula: see text] scalar, a bound for the Higgs potential coupling constant exists and when it is not satisfied, the vacuum is unstable and no nontrivial solution exists. We briefly comment on possible connections of our results with those found in recent dark matter axion models.

scholarly journals Establishment and calculation of the mass gap in three-dimensional SU(1) Yang-Mills theory

1987 ◽  
Vol 189 (1-2) ◽  
pp. 173-180 ◽  
Author(s):  
K. Farakos ◽  
G. Koutsoumbas ◽  
S. Sarantakos
Keyword(s):  
Three Dimensional ◽  
Yang Mills ◽  
Mass Gap
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