Yang–Mills Existence and Mass Gap (Unsolved Problem): Aufklärung La Altagsgeschichte: Enlightenment of a Micro History (original) (raw)

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Yang Mills Theory and Mass Gap

Atomic bonding energies by β-decay and electric and magnetic energies can have mass gap. Their process to the mass gap can be expressed by quantum mechanics of holographical potential energies. Kinetic energy is a circumferential one, which is transitted from radial one. This is a kind of super symmetry. Laplace equation is derived from mass gap condition of quantum mechanics to the radial energy. Kinetic energy and static one (0 2 , − 0 2) make zero point one and harmonic vibrational one. And then the zero point one and the harmonic vibration one make the kinetic one and the static mass (0 2 , − 0 2).

The Physics of Mass Gap Problem in the General Field Theory Framework

E. Koorambas. The Physics of Mass Gap Problem in the General Field Theory Framework. International Journal of High Energy Physics. Special Issue: Symmetries in Relativity, Quantum Theory, and Unified Theories. Vol. 2, No. 4-1, 2015, pp. 104-111. doi: 10.11648/j.ijhep.s.2015020401.18 , 2015

We develop the gauge theory introduced by Ning Wu with two Yang-Mills fields adjusted to make the mass term invariant. In the specific representation there arise quantum massive and classical massless no-Abelian vector modes and the gauge interaction terms. The suggested model will return into two different Yang-Mills gauge field models. Next, we focus on calculating `the meet of the propagators' of those quantum massive and classical massless vector fields with respects to the double Yang-Mills limit. We demonstrate that our proposed version of the Quantum Chromodynamics (QCD) predicts mass gap ∆ > 0 for the compact simple gauge group SU (3). This provides a solution to the second part of the Yang-Mills problem.

Gravity-Assisted Solution of the Mass Gap Problem for Pure Yang–Mills Fields

International Journal of Geometric Methods in Modern Physics, 2011

In 1979 Louis Witten demonstrated that stationary axially symmetric Einstein field equations and those for static axially symmetric self-dual SU(2) gauge fields can both be reduced to the same (Ernst) equation. In this paper we use this result as point of departure to prove the existence of the mass gap for quantum source-free Yang-Mills (Y-M) fields. The proof is facilitated by results of our recently published paper, JGP 59 (2009) 600-619. Since both pure gravity, the Einstein-Maxwell and pure Y-M fields are described for axially symmetric configurations by the Ernst equation classically, their quantum descriptions are likely to be interrelated. Correctness of this conjecture is successfully checked by reproducing (by different methods) results of Korotkin and Nicolai, Nucl.Phys.B475 (1996) 397-439, on dimensionally reduced quantum gravity. Consequently, numerous new results supporting the Faddeev-Skyrme (F-S) -type models are obtained. We found that the F-S-like model is best suited for description of electroweak interactions while strong interactions require extension of Witten's results to the SU(3) gauge group. Such an extension is nontrivial. It is linked with the symmetry group SU(3)×SU(2)×U(1) of the Standard Model. This result is quite rigid and should be taken into account in development of all grand unified theories. Also, the alternative (to the F-S-like) model emerges as by-product of such an extension. Both models are related to each other via known symmetry transformation. Both models possess gap in their excitation spectrum and are capable of producing knotted/linked configurations of gauge/gravity fields. In addition, the paper discusses relevance of the obtained results to heterotic strings and to scattering processes involving topology change. It ends with discussion about usefulness of this information for searches of Higgs boson.

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

Symmetry, 2020

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.

Yang-Mills Theory with a Scalar Field: A Unified Model for Confinement and Mass Gap (Preprint)

International Journal of Research in Engineering and Science , 2023

We propose a new model for the mass gap problem in Yang-Mills theory, based on the introduction of a confinement particle that mediates the confinement force binding quarks together into color-singlet states. Our proposed Lagrangian density describes the confinement particle's behavior and interactions with quarks. We show that the confinement particle naturally explains the mass gap problem, and discuss its implications for nonperturbative phenomena and the renormalization of the theory. Our model provides a new mechanism for understanding the fundamental interactions of quarks and gluons, with potential implications for a range of areas in theoretical physics

Yang-Mills Theory with a Scalar Field: A Unified Model for Confinement and Mass Gap

International Journal of Research in Engineering and Science , 2023

We propose a new model for the mass gap problem in Yang-Mills theory, based on the introduction of a confinement particle that mediates the confinement force binding quarks together into color-singlet states. Our proposed Lagrangian density describes the confinement particle's behavior and interactions with quarks. We show that the confinement particle naturally explains the mass gap problem, and discuss its implications for nonperturbative phenomena and the renormalization of the theory. Our model provides a new mechanism for understanding the fundamental interactions of quarks and gluons, with potential implications for a range of areas in theoretical physics