Hodge Conjecture (original) (raw)

Mass Gap Problem and Hodge Conjecture

I think it could be demonstrated that neutrinos have positive mass working with a non conventional atomic model where two entangled fields that vary periodically create the subatomic particles. I guess that there is some kind of link between the solution of the Mass gap problem and the Hodge Conjecture. I attached a picture at the end for easier understanding the neutrino's mass.

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.

Mass Gap Problem Solution in the Superfluid Quantum Space Model

2021

A given problem in physics can be solved if it is well formulated. Well formulated means that it has a bijective correspondence to physical reality. Mass Gap Problem has no bijective correspondence with the physical reality and is that’s why not solvable mathematically. It can be solved in the frame of quantum mechanics by the formulation of the photon’s mass accordingly to the Planck-Einstein relation.

Position-dependent mass, finite-gap systems, and supersymmetry

Physical Review D, 2016

The ordering problem in quantum systems with position-dependent mass (PDM) is treated by inclusion of the classically fictitious similarity transformation into the kinetic term. This provides a generation of supersymmetry with the first order supercharges from the kinetic term alone, while inclusion of the potential term allows also to generate nonlinear supersymmetry with higher order supercharges. A broad class of finite-gap systems with PDM is obtained by different reduction procedures, and general results on supersymmetry generation are applied to them. We show that elliptic finite-gap systems of Lamé and Darboux-Treibich-Verdier types can be obtained by reduction to Seiffert's spherical spiral and Bernoulli lemniscate in the presence of Calogero-like or harmonic oscillator potentials, or by angular momentum reduction of a free motion on some AdS 2-related surfaces in the presence of Aharonov-Bohm flux. The limiting cases include the Higgs and Mathews-Lakshmanan oscillator models as well as a reflectionless model with PDM exploited recently in the discussion of cosmological inflationary scenarios.

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.