1. The concept of the UFT quanta systems in a nutshell

The definitions of each quanta system is based on two sets of appropriately defined of quanta numbers: the set of quanta numbers defining the quantum element itself and the corresponding quanta numbers of the related “dynamic” anti-particle. The difference of those two sets of quanta numbers defines the quanta numbers of the “wholeness” of the overall quanta system. Technically spoken, this difference is used to define the intrinsic potential (the indefinite norm) between quanta and anti-quanta. The corresponding Krein space based selfadjoint  J-symmetric) potential operator defines the quanta system specific dynamic energy inner product and dynamic energy norm.

There are two groups of dynamic quanta systems:

Quanta systems group 1

The quanta systems with sets of quanta numbers less than one. Those quanta systems represent purly dynamic “particles”. Group 1 enables 2-component purely dynamic quanta systems with the minimal possible dynamic energies compared to all other systems. The group 1 quanta systems provide the a priori (!) concepts of “ground state energy” and “perfect plasma energy”. In this sense they are meta-physical concepts. They enable the building of the composed “particles” of group 2, (basically governed by “number theoretical Schnirelmann probability”).

Quanta systems group 2

The quanta systems with sets of quanta systems with quanta numbers greater than 1. There is only one quanta system with a constant quantum number one, the neutron quanta system, which we also assign to this group.Those quanta systems represent mechanical “particles”. Group 2 enables a posteriori mechanical (explicate) particles equipped with intrinsic dynamic energy. The most relevant “first” of those particles is the “electroton”, which corresponds to Dirac’s “free electron” particle. Its natural mechanical partner becomes the “Magneton”. Both particles may appropriately composed to “electronium”, “positronium”, and “neutronium”. All related 1-component quanta systems are called Dirac 2.0 systems. In order to build an appropropriate framework to apply the “ground state” and “perfect plasma” energy fields to explain the creation of stars we additionally proposed a 2-component mechanical perfect electromagnetic quanta system built by a 2-component (mechanical) electroton - magneton quanta system.


2. The UFT quanta scheme making gauge theories obsolete

E. Fermi: "Dirac's theory of radiation is based on a very simple idea; instead of considering an atom and the radiation field with which it interacts as two distinct system, he treats them as a single system whose energy is the sum of three terms, one representing the energy of the atom, a second representation the electromagnetic energy of the radiation field, and a small term representing the coupling energy of the atom and the radiation field", (FeE).

The central new paradigm enabling the deductive quanta systems scheme are two quanta system specific self-adjoint, positive definite operators on the full Hilbert space with compact inverse operators. They enable the definition of related mechanical and dynamic inner products and definite norms on the full considered Krein-Hilbert space. In terms of Dirac's single system model the mechanical energy part represents the mass energy of the atom and the dynamic energy provides its radiation (interaction) field, while the anyway neglected coupling energy is no longer required.

Colloqially spoken, it looks like that the gauge theories want the explain Nature what she is doing wrong, while the UFT based dynamic quanta systems scheme explains from a theoretical understanding Nature's energy conservation laws based on meta-physical (mathematical) a priori axioms (the ground state field and the perfect plasma field accompanied by a hidden complex Lorentz group symmetry).

Quote from R. Courant: „Empirical evidence can never establish mathematical existence – nor can the mathematician’s demand for existence be dismissed by the physicist as useless rigor. Only a mathematical existence proof can ensure that the mathematical description of a physical phenomenon is meaningful“, (HiS) p. 148.

Quote from D. Neuenschwander: "The common denominator of those three theories of the SMEP is the quantum mechanics, which is based on an axiomatic structure in a Hilbert space framework", (NeJ).


Further notes

Note: The Yang-Mills theory is the generalization of the Maxwell theory of electromagnetism, where the chromo-electromagnetic field itself carries charges. As a classical field theory it has solutions which travel at the speed of light so that its quantum version should describe massless particles (gluons). However, the postulated phenomenon of color confinement permits only bound states of gluons, forming massive particles. This is the mass gap. The physical ("color") confinement challenge is that the phenomenon that "color-charged" particles (such as quarks and gluons) have not been isolated until today. Another challenge of „confinement“ is asymptotic freedom which makes it conceivable that quantum Yang-Mills theory exists without restriction to low energy scales.

Note: In classical mechanics one deals with the three scales, „distance“, „time“, and „mass“; in non-relativistic quantum theory and classical relativity one deals with two scales, „distance“, and „time“; in relativistic quantum theory one deals with only one scale, the „distance“, (DeP) p. 551.

Note: (renormalization group equation and symmetry break down): The behavior of a physical system depends on a scale (of energies, distances, momenta, etc.) at which the behavior is studied. The change of behavior when the scale is changed, is described by the renormalization group equation. In quantum field theory, the dependence of the behavior on the scale is often expressed mathematically by the fact that in order to regularize (i.e., render finite) Feynman diagram integrals one must introduce auxiliary scales, cutoffs, etc. The effect of these choices on the physics is encoded into the renormalization group equation. The "case" if there is no related (G-invariant) renormalization realisation (example ground state energy) is called "symmetry break down", (DeP1) p. 1119 ff..

Note (Symmetry and permanent elementary particles): According to the “Big-Bang Theory” in the early universe pressures and temperature prevented the permanent establishment of elementary particles. None of the invented elementary particles of the SMEP were able to form stable objects until the universe had cooled beyond the so-called „supergravity phase“. „Symmetry“ is thought of as an overall governing concept already existing during the chaos and flux of the early universe, before and during virtual particles are created and destroyed until today. This „symmetry“ concept is accompanied by the concept of a „time symmetric, mirror-like quality to every interaction in the early universe“. Physical conservation laws governed by this „symmetry principle“ limit the possible interactions between particles. Imaginary processes that violate conservation laws are forbidden. So the „existence of symmetry“ provides the source of order to the early universe.

Note (Determining nuclear spin): Each nucleus has an intrinsic angular momentum which interacts with angular momenta of electrons or other nuclei. It is measured in units of the Planck constant and, according to quantum mechanics, can take only integral or half-integral values. Three methods of determining nuclear spin are, (BeH) p. 19.

Note: Gauge bosons arise spontaneously without external influence and you can freely select certain parameters locally without anything changing of the related interaction.

Note (The Higgs mechanism): „The Higgs mechanism of spontaneous symmetry breakdown allows gauge fields to acquire mass. In spite of these refinements, the basic fact remains that the existence of gauge fields is a consequence of the existence of gauge-invariant action densities for particle fields“, (BlD) xi. It builds on an extended from global to local U(1) transformations symmetry group of the underlying Lagrangian. It explains the mass of the gauge W- and Z- (weak interaction) bosons of the weak “nuclear-force”.

Note (free-electron theory and an infinite resistance of insulators): Insulators show a specific resistance to electricity which may be  times greater than that of metals, which is a phenomenon never properly understood on the basis of the "real theory, (WiE).

Note: The common conceptual denominator of the quanta systems groups 1 and 2 are the intrinsic dynamic energy inner product and dynamic energy (definite) norm.

Note: The intrinsic dynamic energy part of a quanta system during the building process of composed quanta system decreases, while the mechanical energy part increases. Accordingly, an overall action minimization concept across all deductive structured quanta scheme governs  a “particle” decay process finally back to the ground state.

Note (regarding Bohm’s notions of “wholeness”, “explicate and implicate orders”): The wholeness is described by the quanta system itself, the explicate (observable) “particles” are described by group 2. In group 1 there are only implicate (unobservable) “particles”, which also arise as implicate (unobservable) “particles” as “anti-particles” in group 2.

Note: “Invariant” means that a quantity’s numerical value is not altered by a coordinate transformation. “Conserved” in contrast, means that within a given coordinate system the quantity does not change throughout a process. “Invariance” compares a quantity between reference frames. “Conservation” compares the quantity before and after collision or reaction or process within a reference frame. Noether’s theorem relates conservation to invariance, and thus to symmetry, ” (NeD) pp. 1-4.

Note: The invariant quantities in energy conservation laws are governed by functionals. In a Hilbert-Krein space framework such functionals are definite and indefinite norms. “Functional integrals” are defined by the Krein-Hilbert space intrinsic hermitian operator.

Note: The quanta system intrinsic hermitian potential operator enables a Hilbert space based definition of the new dynamic energy concept,which is complementary to the mechanical (kinetic and potential) energy concept. It avoids the concept of case specific potential functions.

Note: The two hermitian (mechanical and dynamic) operators of 1-component mechanical Dirac 2.0. systems avoid the concepts of fermions and bosons.

Note: The observable mass of a free electron is the sum of its naked mass and its self-mass. Both of those masses are unobservable. However, self-mass occurs in the scattering matrix. All workarounds to overcome this discrepancy become obsolete, if the self-mass is interpreted as the intrinsic dynamic energy of an electroton.

Note: The positron and the electron have similarity with the W(+) and the W(-) bosons, and the photon boson has similarity with the Z boson.
 
Note: Quote from R. Feynman: "Pauli's spin matrices and operators were nothing but Hamilton's quaternions", (UnA2) p.153.

Note: Quote from A. Unzicker: "All in all, there are many indications that electrons, including their strange spin behavior, are described more simple by S(3). In any case, despite the elegant representation Dirac had developed, it cannot be claimed that this sheds light on the reason for the existence of spin", (UnA2) p. 183.

Note: The quanta system intrinsic hermitian potential operator defines corresponding norms. The existence of invariance reveals an underlying symmetry. The change process of the beta-decay is described by the symmetry group SU(2). The symmetry group SU(2) is isometric to the unit quaternions S(3). A quaternion rotation operator rotates a 3D vector v in such a way, that to resulting vector w is a rotation of v by twice the angle of the quaternion q, around the axis defined by q’s vector components.

Note: The (real) restricted Lorentz group associated with SU(2) becomes the candidate for the symmetry group of all mechanical 1-component quanta (Dirac 2.0) systems (accompanied by appropriately defined intrinsic (anti-) dynamic quanta systems). Accordingly, the complex Lorentz group (i.e., the hidden symmetry group of the Coulomb problem) becomes the candidate for the symmetry group of the 2-component quanta systems.