The Origin of the Color Charge into Quarks

Showing the origin of the mass in an additional coupling between field quantum oscillators, we formulate a hypothesis of a geometrical structure of the oscillators of “fields-particles”. In this way, we define the possible structure of quarks and hadrons (as the proton). This hypothesis is reasonable if one admits field oscillators composed by sub-oscillators at semi-quantum (IQuO) and in which a degree of internal freedom is definable. Using the IQuO model, we find the origin of the sign of electric charge in to particles and, in quarks, the isospin, the strangeness and colour charge. Finally, we formulate the structure of the gluons and the variation modality of the colour charge in quarks.


Introduction
If we associate a wave behaviour to particles, you see the diffraction with electrons and photons, one can conjecture that "something" oscillates "inside" a particle. This conjecture is plausible even if the positivist literature has set aside it, because this is not directly verifiable with experiments. Instead, by this hypothesis, we could talk about internal "clock" with proper frequency (ω 0 ). On this basis, we could say that "the time is inside the particles". In the same way, then we could discuss about Compton wavelength ( c ) or the spin of the particles, as something of "space" "inside" these. All that pushes us to affirm that "the Space-Time is inside the particles". Since we always speak of particles being in space-time (ST), you see the conception of frame reference, thus we can say that particles and Space-Time define reciprocally themselves and if particles are also the concept of energy a rest. So we can speak of mass-energy like the energy of movement in time: all this is coherent to relativity. This uniform motion in time recalls once again the "clock" that exists inside every particle-object as a periodic "motion". With proper frequency (ω 0 ), which corresponds to [ω 0  τ], where (τ) is the proper time. The proper characteristic of a massive particle, associated with the proper time (τ) of an object, coincides with the proper mass (m 0 ) of that object. Then, discussing the mass or mass-energy of a particle, it is the same that to consider the time of the clock which is inside them [ω o  τ  m o ]. Then, based on QM [1]: If the frequency ω 0 generates the proper time τ of a massive particle [τ = /mc 2 ], then for symmetry, there exists a wavelength  c that originates the "proper space" of the particle [1]. Following De Broglie, we have: As is well known, this equation describes the oscillations in a set of pendulums coupled through springs [3] and scalar fields associated with massive particles with zero spin: We conjectured [3] that mass is a physical expression of the proper frequency (ω o ) related to a particular elastic coupling, which is in addition to the one already existing between the oscillators of the massless scalar field (Ξ). This "additional coupling", which produces the mass in a scalar field (Ξ), has been referred to as a "massive coupling" [7]. Then, we conjectured that the massive particle-field (Ξ) is originated by a "transversal coupling" (T 0 ) between the chains of oscillators of the scalar base field (Ξ). All that can be represented in way figurative as shown in Figure 1. Therefore, a massive particle can be represented by lattice with transversal coupling on an Ξ-scalar field. The massive particles are so constructed by the massive additional coupling which translates the "internal structure" of "coupled oscillators" into a geometric form.

Hypothesis of Structure
The massive particles are so originated by means of the massive additional coupling which builds the "internal structure" of "coupled oscillators" in geometric form.
A first geometric form we can find into proton considering an apparent coincidence between the Compton's wavelength of Planck's particle and the one of the proton. Following this coincidence and the "Hypothesis of Structure" [2], one can describe a proton as having a pentagonal geometric structure in which the constituent three quarks are coincident with three internal triangles (see the following Figure 2): The vertices (A, B, C) are coincident with the three centres of diffusion in the interaction electron-proton. The structure is so because one high lights an "aurea" (golden) relation between the proton and Plank's particle. Recall (see Figure 3) the "aureus" (golden) segments: By property of the "golden segment" one has: where (ϕ) is the "aureus" number. If we denote now with n (pl,p) the experimental numerical ratio between the Compton's wave length ( pl ) and ( p ), experimentally it's:   Then by Equation (2.6), we note there is an "aurea" relation, less than a factor (10) p between the proton and the Planck particle. In universe where the space-time is in expansion the spatial relations between some geometric structures could "dilate" increasing in scale. So we assume that a particular spatial relation between particles could be invariant to any scale. Therefore, we could state that a proton is an "aurea" particle because it follows the relation (2.6a); in this way, we can consider the three quark which compose it as three "aureae" triangles [(u), (u), (d)]. The same, using the Hypothesis of Structure, a quark can be represented by three elastically coupled quantum oscillators. This hypothesis could allow us to represent [1] the (u, d) quarks as structures of coupled quantum oscillators, you see the Figure 2. The representative structure [1] is similar to one of three "spheres" placed at the vertices of an aureus triangle and connected by "springs" ("junction oscillators"). Nevertheless, these structure can be possible (see [2] [3]) only if we use particular quantum oscillators defined "IQuO" (acronym of Intrinsic Quantum Oscillator). Besides, we need adding that the three quantum oscillators need to constitute an individual physical object, i.e. a quark, and this says us that we cannot separately detect the IQuO, as shown in Figure 4.
On these ideas, we discussed the "sub-structure" of quarks, which is applicable only to "particular" quantum oscillators (IQuO). This "particularity" is underlined in the necessity that the vertex-oscillator to connect to the other vertices trough junction oscillators has to be able to have in turn a structure of "hooks".
All that induces us to talk about a "sub-structure" into quantum oscillator: we so need having an oscillator with more components. An oscillator of this type is highlighted only into quantum oscillator coupled to other oscillators. In fact, in the oscillation theory two coupled oscillators influence each other as if they are two "driven" oscillators. Just in a "classic" driven oscillator is highlighted a  "structure" of components such as the "elastic" component and "absorptive" [3].
Therefore, this quantum oscillator with two components allows us to talk about a more elementary structure of it.
Another indication of a "composite structure" in quantum oscillator derives from its wave function (see Figure 5): In fact, the quantum oscillator (with n the quantum number and n = 1) shows a wavefunction (Ψ) with a pair of peaks in the probability of detecting the energy quanta of the oscillation: we can describe therefore the quantum oscillator with two sub-units of oscillation or "sub-oscillators". Into quantum oscillator with (n = 2) there are three peaks in wave function (Ψ) which denote three sub-oscillators (see the Figure 5).
Not only, but two components in an oscillator encourage us to believe that the energy of the "quanta" is distributed between the two oscillating components.
We think the presence of two components in an oscillator causes the splitting of its quanta of energy into two energetic components in each sub-oscillators: this introduces the idea of "semi-quanta" (or individually "semi-quantum"). A quantum oscillator with a sub-structure made of sub-units of oscillation, or "sub-oscillators" and "semi-quanta" is called "IQuO" [2].

The Quantum Oscillator at "Semi-Quanta"
We will explain the origin of the IQuO concept. The elastic couplings of field quantum oscillators transform each quantum field oscillator in a coupled oscillator. Therefore, each field oscillator acts as a "driven" oscillator, which, following oscillations theory, is described by two components: the absorptive amplitude (or "inertial" amplitude) and the elastic amplitude. By using ( [2] [8]) operators in phase plain (q, p) we derive the following equation: Thus, [2] [3] [8] we can represent an oscillator as described in Figure 6.
Therefore, in a driven oscillator two components are highlighted: the "elastic" and "absorptive" components [3] [5] [8]. It is important to note that any type of driven-damped oscillator as well as the ones elastically coupled-to-other-oscillators, show a solution of the motion equations comprising of two oscillating components. These components are defined as "elastic" and "inertial" (or absorptive).   This hypothesis of field quantum oscillators may seem "extreme"; however, we observe that in the electromagnetic interactions a photon "forces" an electron: at the point (P) of interaction the individual quantum oscillator of the electronic field is driven by the individual quantum oscillator of the electromagnetic field (photon). In this case the electronic field oscillator is described by two This double structure of the operators (a, a + ) splits the energy quanta of the quantum oscillator, giving: A structure with two sub-oscillators involves that when the energy "quantum" is in one of two sub-oscillator the other sub-oscillator cannot be empty of energy but having the value of (ε = 1/2hν) defined "semi-quantum" (remember [ε (n=1) = (1 + 1/2)hν)]). A structure with two components (elastic and "absorbing" or inertial) and two sub-oscillators would say that the "quantum" is composed by two (ε = 1/2hν) semi-quantum. Then we conjecture energy values of [(ε = 1/4hν)], indicated as "empty semi-quantum" and symbol (o), and another [ε = (1/4hν)], indicated as "full semi-quantum" and symbol (•). We will obtain the probabilistic representation of the "semi-quantic" oscillator at a given instant ( Figure 7).
Here, there is a synthesis: Then the Equation (3.1) in IQuO-representation will be:

t a t a t a t a t a t
ω ω ω ω where (r' = ±1) is connected to the direction of phase rotation.
For (r' = +1) the two equivalent representative ((2 rows) × (2 columns)) matrices (see Equation (3.1)) are: Omitting the time and the phase but highlighting the rotation direction (clockwise (cl)-anticlockwise (cl)). Besides, remember that inertial component is shifted to (π/2) by the elastic component. There are different configurations of IQuO in the pairs ((•), (o)) but all equivalents, as: An IQuO (see Figure 8) can so have the following graphically representation into phase plain (q, ip), see [2] [3]: Because two sub-oscillators compose the oscillator, going in the representation of wave function scalar (Ψ(x(t)) and highlighting the phase rotation, we will obtain a bi-dimensional representation of oscillators with ( ) ( ) It will be graphically (Figure 9(a)) and into instant: Note that the configuration is variable to the pass of time.
The next configurations (Figure 9(b)) can be the following:  The 8-configuration will coincide with 1-configuration.
In the matrix representation, omitting the time and phase, this configuration is: where (o el , • in ) is the couple with anti-clockwise phase rotation, while ( ) Using the (⊕) combination operation [2]: where the right side of Equation (3.8) contains the two representative matrices of the Ψ-IQuO and the Ω-operation defined as: G. Guido Journal of High Energy Physics, Gravitation and Cosmology Then it is: Note the X-operation is derived by associative property of addition (you see the Equation (3.5)): Graphically, the final result ( Figure 11) is:  not happens in any point (see Figure 11): the Ψ-IQuO is so essentially different from Φ-IQuO. We called Ψ-IQuO type as "Fermion" while Φ-IQuO as "Boson". That is because we think that the IQuO are the fundamental quantum oscillators of all fields-particles.

The Electric Charge
An advantage in treating the field oscillators using the IQuO is that the "2-dimensional" representation ( Figure 9) allows us" to distinguish the direction of rotation of the phase associated to oscillations having an only direction of phase rotation". In fact, taking into account both the distribution of semi-quanta inside the two sub-oscillators of an Φ-IQuO (I 1 ) and both their movement concerning the phase, another IQuO (I 2 ) in coupling with first IQuO (I 1 ) it could detect the direction of rotation of the phase of (I 1 ).
Note that IQuO I 2 (Ψ-type) could be the representative quantum of a particle of interaction (i.e. photon). So, the direction of rotation of the phasedetermines a new degree of freedom in a quantum oscillator with semi-quanta. This degree of freedom admits two possibilities that would be interpreted as "the sign of the electric charge" of a particle. We conjecture that the IQuO [(Φ anti−cl ), (Φ cl )] can represent particles with opposite sign of electric charge [2]. This important result marks a turning point in the understanding of the physics of the interactions. We recall that the electric charge is in correlation with the generator of gauge transformation SU(2) which Pauli's matrix is (σ 3 ) [7] [8]; so, we can derive the Q electric charge from the following equation, using the matrices (Φ) of the Equation (3.12): Using the well-known definition of the electric charge [2] and the commuta-G. Guido Journal of High Energy Physics, Gravitation and Cosmology tion relations with semi-quanta (see Equation (3.4) Appendix in [2]) it then follows that: Note, besides, the conjugation operation transforms the semi-quantum operators:

The IQuO(n=0)
The vacuum state of an "isolated" IQuO (n=0) will be graphically represented ( Figure 12): Even here we can have some possible representations.
One of these (A-representation) can be the following ( Figure 13): With representative matrices (2 × 1): The conjugate representation ( Figure 14) is: And the conjugate matrices: We note that the two possibilities (G 3a , G 3b ) are indeed one only possibility because (G 3a ) + = (G 3b ); then we admit one only possibility → (G 3 ) A . We obtain: ( Figure 15) With representative matrices:         or a combination of them (see the 3.17a). We'll have the following representation ( Figure 18 and Figure 19): We call the IQuO (n=0) as IQuO-0.
If we call the three internal degrees of freedom (G i ) as "color charge" then we

The Electric Charge of Quarks
As we know the abstract space to describe the hadrons, requires the transforma- The λ 3 matrix is the projection in SU(3) of Pauli's matrix σ 3 , giving [2] the values of Q in the representation of the eigenvectors basic (Φ + , Φ − ). We recall (in Gell-Mann theory) the correlation between Y and the matrix λ 8 : Giving the correlation between the charge Q and the isospin T 3 and Y, we can G. Guido Journal of High Energy Physics, Gravitation and Cosmology In conclusion, the matrix ( 3 ) can tell what values are allowed to charge Q of a quark.
Then we think the IQuO of quark is expressed by matrix (1 × 3). In fact, if we recall the form of the wave function (see Figure 5) of the quantum oscillator with (n = 2) where there are three probability peak, then we can think that a IQuOI (n=2) is made with three sub-oscillators. The superposition of two IQuO I (n=1) or (I 1(n=1) ⊕I 2(n=1) ) builds an IQuO ( . Note that to make couplings between sub-oscillators of two IQuO different it needs the exchange a full semi-quantum between the two respective component oscillators: this is allowed by a reciprocal intersection between the two IQuO (see Figure 21): So, we need to define an operation (⊗) stating an appropriate combination of two matrices [(2 × 2) and (2 × 1)] generating one matrix (2 × 3). Using the matrix representation: where index c indicates the couple of semi-quanta of the central sub-oscillator in Figure 21 and where [(α˚ = α + π/2), (ρ˚ = ρ − π/2), (σ˚ = σ ± π/2)].
It follows [2] the electric charge of IQuO (n=2*) :  As mentioned this couple is representing the color charge.

The Isospin
Taking up the idea of "internal" rotation of the phase [2] into IQuO, further "internal" rotations into a "composed" particle (as is a hadron) could be identified [1]. Remembering the electric charge connected to rotation of the phase of an IQuO (as "internal" rotation), we could connect the isospin (since it has similar structure to that of the "spin") to an "internal rotation" of "something" existing "inside" the hadrons.
As you well know, the transformations between hadrons show the existence of multiplets. Besides the "organization" of hadron in degenerate multiplets in mass and they internal transformations between hadrons prove that the hadrons are composed by "more elementary" particles called quarks. Thus the existing "rotation" inside a hadron could relate well to quarks; if the spin of a quark regards its spatial orientation, the isospin cannot regard to ulterior additional spatial orientations. Then we could assume that the "isospin rotation" could be correlated to the "rotation" of the internal current of "semi-quanta" that interconnects the quarks constituting a hadron. Remember the correlation between representative matrices of spin (σ) and isospin (T). Besides, it can note that in Hadrons exists a correlation between the charge Q and the isospin T 3 .

G. Guido Journal of High Energy Physics, Gravitation and Cosmology
Remember that matrix σ 3 is also used to represent the projection (T 3 ) of isospin T in the complex space Q (2). In fact, it's: 3 3 1 0 0 This formal analogy between σ i e (T i ), as between σ 3 and (T 3 ), cannot be random.
Also, note that the formal analogy between (T 3 ) and the spin of a composite particle induces assign a value of (T 3 ) also to the quarks.
It is recalled in fact the summative character of the isospin, then it follows that the isospin of a hadron is the sum of the values of isospin assigned to each individual quark.
Furthermore, the correlation between T 3 and Q, leads us to admit the existence of a correlation between the direction of rotation of the phase and the one of the isospin current.
This clearly happens in individual quarks, because there are the following associations:

3) External Spatial rotation of spin (σ sign)
This may seem at odds with the "spatially local" aspect assigned to the elementary particle (like quarks and leptons), in perfect agreement with the relativistic quantum theory. However, considering what already talked about the rotations inside to hadron and taking into account the phenomenology of the interactions between hadron, it can become acceptable assume the following hypothesis of Structure: even if an elementary particle proves to be a "local unit" in space for an external observer, it may instead show the existence of an "internal" space because described by variations of physical quantities that can be identified as "internal" rotations showing an "internal structure" of couplings of IQuO.

If the isospin (T h ) assigned to a hadron identifies an internal current
(semi-quanta current or "gluonic" current) then the isospin (T q ) assigned to a quark identically detects a semi-quanta current that identify a "path" between elementary "internal points of oscillation", though always considering a quark as an "oscillating" unique physical system.
A quark, though maintaining the external aspect of an energy quantum in a space point, could instead be constituted by an internal structure of "virtual" "IQuO called" Sub-IQuO". This "virtual" internal structure of a quark has a descriptive index that we individualize in the Hypercharge Y. The latter, as well as Journal of High Energy Physics, Gravitation and Cosmology being introduced to differentiate the hadron multiplets, is assigned to an individual quark, reinforcing the idea of its sub-structure related to different configurations of coupling of sub-IQuO that make it.

The Hypercharge Y
Another support for this hypothesis of Structure is identifiable in the correlations between the "internal" rotations (those of phase and isospin) during the hadron interactions (you see Clebsch-Gordon coefficients).
It was noted that Q and T 3 have the same algebraic sign; this implies that the isospin current between "Sub-IQuO" constituents of a quark follows the with the probability that a photon detects the quanta of the charged particle which has a particular structure of sub-IQuO. If into electron this probability has a value equal to one, the probability in quarks has not an integer value because the triangular structure of a quark has a number of quanta minor that the number of sides. If inside a quark there are more sub-IQuO, the photon in coupling with one of sub-IQuO components cannot find the representative quantum of the quark. For the definition of statistical probability, if a quark may be no seen by a single photon, then it will be not seen by an infinite number of photons. How to say that a quark would be invisible to single photon.
However, if the single quark cannot be seen, a hadron composed by more quarks can be detected only if the sum of the probability of finding the quantum has a value of a unit or the sum of the electric charges of the quarks of a hadron reaches the value of a unit. This is because two or three quarks bound to become a single unit (or a single center diffuser) for couplings with photons.
The information of the non-integer value of the electric charge of a quark can G. Guido Journal of High Energy Physics, Gravitation and Cosmology also be found in the Gell-Mann matrix λ 8 , which is an expression of the connection (Q ←→ Y). In fact, (see the equation 3.19) it is no random coincidence that the matrix λ 8 precisely commutes with the λ 3 (you see σ 3 ). In [1] so note that the eigenvalues of Y are related to the values of electric charge Q. Obviously, everything is perfectly in accord with the relation: [Y = 2(Q − T 3 )]).
Therefore, we think that the quark is given by one "triangular" structure of three "sub-IQuO" (see IQuO-vertices) coupled to each other through IQuO chains (sides) in which flows a current of semi-quanta. The variable descriptive of the semi-quanta current is the Isospin (T) whose projection (T 3 ) is connected to the rotation direction of the current, we have the following correspondence: The variable descriptive of the phase rotation in IQuO-vertices is electric charge Q: By triangular structure of the couplings, it follows that the direction of rotation of the semi-quanta current along the sides shall be concordant with the direction of rotation of the phase of IQuO-vertices. This expresses the correlation (Q  T 3 ). Also to its structure, it shall be associated with descriptive variable that we believe it is the Y (hypercharge). It is evident that the probability of finding the quantum of a particle inside of a structure depends on this latter. As the value of the electric charge Q has been associated with the probability of detecting the representative quantum of the quark, it follows the (Q  Y) correlation. The correlation (Q  Y  T 3 ) is now: We ask in what way the Y is related to the structure. A triangular structure of IQuO-V coupled suggests that get involved more chains of IQuO and therefore it should exist the possibility to realize a coupling "transverse" between separate chains. Chains involved in the triangular closure defining a quark can be in a number of two or three at the most (you see the Figure 7 and Figure 8).
For everything that we affirmed up to now, we can say that the hypercharge Y is the indicating physical variable the triangular structure of coupling of Sub-IQuO vertices to which we associate the value 1/3 as to say that there is one particle-quantum on three vertices. Also, noting that a triangle in the mirror (P) undergoes inversion right -left, we assign the value of the hypercharge Y = −1/3 to the antimatter. We note that the direction of rotation of any rotating object

The Coupling of Chains
If to an only oscillator (quantum and classic) we assign an elastic component (see a el in quantum oscillator) which represents the elastic tension (k) acting on the "mass" (M) of oscillator (see a in ), to the chain of coupled oscillators we assign [1] the same elastic tension (k) between oscillators (see Figure 1). The same aspect is in the two sub-oscillators which component the IQuO. In summary: so as two sub-oscillators couple for making an only IQuO, then it is possible that more IQuO couple for making up a "chain" of coupled quantum oscillators. To chain (see Figure 1) is assigned an elastic tension T: [k∆l]. We think that can be possible the following representation of chain ( Figure 22): Note (see Figure 8 and Figure 9(a)) that the semi-quanta oscillate (•) inside each IQuO: the couple ((•), (•)) would oscillate always only between the points (A, C) in IQuO 1. Nevertheless, it is necessary even that the couple ((•), (•)) propagates along the X-axis: the propagation from IQuO-1 to the next (IQuO-2) needs so to oscillate with variable frequency (ω). To have both propagation and oscillation of couple ((•), (•)) it needs a superposition with another chain, but shifted (of π/2): this could allow an oscillation of the full semi-quantum couple ((•), (•)) inside a sub-oscillator of IQuO and after the propagation along axis X. In first we report the figure of two IQuO (you see Figure 23) in a particular overlap: We note that two IQuO overlap and sharing the sub-oscillator central. Two IQuO can exchange energy only in the point C of the central sub-oscillator. The operation of superposition is indicated by (⊕): (⊕) is the overlap of two IQuO involving an only sub-oscillator of two IQuO (see Figure 23).
We note the exchange [(a in )(•) → (A in )(o)] happens in point C of the configuration; these exchanges make oscillate the couple ((•), (•)) inside central oscillator just once because after it happens the passing to first sub-oscillator of the 2-IQuO.
In this way, the quantum ((•), (•)) can propagate with oscillations along the chain and so to constitute a "field chain". It follows any field can be represented by a set of "field chains". In the case of closed chains (see the sides of a triangular structure) then the superposition of two chains in each side is the fundamental condition for having the oscillating propagation of couple ((•), (•)) along the sides. It is evident that this determines even the "isospincurrent" inside the triangular structure of quark.

The Quark Structure
A structure of IQuO coupled oscillators can even involve at least two or most distinct chains of IQuO. It's evident that the coupling between distinct chains of IQuO can be built with the help of "transversal" chains ( Figure 24) which "intersect" them and form so an additional coupling, you see the massive coupling (see par. 1). Graphically: The transversal IQuO represent the "massive coupling". So the structure in Figure 24 will be represented (see Equation (3.10)) by matrix (see Figure 11 This is a column matrix; the square brackets will indicate the IQuO of massive coupling. Note that inside in any chain with massive coupling there are IQuO of type "Boson" (see the Figure 9). An elementary "geometric structure" involving "three" chains of IQuO can be given by "isosceles triangles" (you see Figure 25 An IQuO-V in order to belong to a chain and to the triangular structure of the couplings has to be an IQuO (n=2*), with three sub-oscillators but with only three full semi-quantum (•)). This is because its sub-oscillators can so overlap to the sub-oscillators of the junction IQuO or IQuO-J (the three IQuO: I AC , I BC , I AB ) connecting the three vertices. To achieve this, in analogy with the physical system "springs-spheres", it is necessary to have (Figure 26): Journal of High Energy Physics, Gravitation and Cosmology   Note well that in this figure for clarity are not shown the connecting IQuO-J. As we have already said, the geometric coupling structure can express spatial "orientation" or "spin" and, the same time, to propagate in space. There are more descriptive possibilities: 1) The vertices (I B ) and (I A ), you see the Figure 26, are detached from the respective chains (1 and 2) while the vertex I C is connected to the chain 3. In this case the structure can rotate around the direction of the chain 3, where it is in moving.
2) Each vertex moves along its own chain and the spin will be given by its particular IQuO vertices of the structure.
Nevertheless, we could consider these two representations as equivalents.
The representative matrix of IQO-V (with n = 2* because it is composed by 3 sub-oscillators with 3 full semi-quanta (•)) will be (see (3.23)):  So, an any IQuO (n=2*) is represented by a column matrix with three elements.
If three transversal chains crossing reciprocally it is possible to form three IQuO-V. Having the oblique chains it is possible that there are some shifts in respective IQuO-V components: there is the possibility that an IQuO-V (n=2) is formed but with three sub-oscillators not aligned. This can generate component sub-oscillators in vacuum state (n = 0): Nevertheless, to keep the three chain connected then it is needed that in the longer sides-chains there are IQuO (n=2*) . So note that the two oblique IQuO-J should be longer than that of the base: if IQuO-side (n=2*) then IQuO (base) (n=1*) .
The IQuO of connecting (IQuO-J) should be so constituted by a central sub-osc. and two lateral sub-oscillators: these last are overlapping of the lateral sub-oscillators of the IQuO-V. This could cause a discontinuity in the flow of the semi-quanta within IQuO belonging to quark. Instead, it is needs to have a continuous flow of semi-quanta long the sub-oscillators (you see the isospin), namely all sub-oscillators must be of the same type and to have the same number of semi-quanta. So, to achieve a continuum in the flow of semi-quanta it is necessary to have a side with double chain or, in the same way, it is necessary to double all the sub-oscillators which compose the connecting lines of vertices (see Thus we'll say that a quark is a structure of sub-oscillators. Besides, during the quark formation, the coupling between two vertices (A, B) and the chains (1, 2) could break: it could happen that the two chain (1 and 2) can break away from the IQuO-V (I A , I B ). The quark structure could remain instead intact with the possibility of propagation along axis X (3-chain). As we said, this possibility allows, for symmetry, a "spin" of the quark around axis X (3-axis). The quark can tie with other quark along a side [4] as the BC, forming a hadron; in this case, the IQuO I A remains free and, for rotational symmetry, one can associate a rotation (spin) of the triangular structure of quark around to (BC)-axis, which becomes the chain of propagation of new hadron.
Note that in forming a quark the elastic tension along sides can be different in the some points, see the Figure 28: The k-elastic tension of sub-oscillator of the IQuO [(I CH ), (I C ), (I FC )] is more rigid (k C > k B ) than in I B and I A , because the C-vertex is attacked to the chain while the vertexes A and B are now free. Note that when we apply the same force to the ends of two attached springs, but different in elastic tension, then we will see that the spring with the smaller elastic tension is longer than the spring with the greater elastic tension. In this way the sub-oscillators [(BH), (B), (BD), (AD), (A), (AF)] are stretched. If (BH = l(1/2)), then we could admit: where (ϕ) is the "aureus" number. Besides For compatibility has to be the case that This aureus ratio defines an "aureus triangle" with vertex angle of (72˚) and these structures of coupled IQuO will define the "aureus structures" of the quarks

The Quark Structure (u, d)
Now we formulate the following hypothesis (see also [3] [4]): an "aurea" triangular structure of coupled quantum oscillators (IQuO) with vertex angle of (72˚) corresponds to the quark (d). From the ( Figure 27) and ( Figure 2) we derive, shortly and schematically, that (see Figure 29): Where ( d ) is the wavelength Compton of d-quark. Recalling the pentagon ( Figure 2), we assume that the "aureae" lateral triangles could represent the quark (u) (see [1] [4]). The graphics "relation" between the quark (d) and (u) will be ( Figure 30): Where ( u ) is the wavelength Compton of u-quark, with C-vertex angle of (104˚).
We have already said that the quark is an overlap of IQuO-V and transversal-IQuO(see Figure With representation ( Figure 31).

The Gluon
We can think that there are different possibilities of combinations between IQuO-0 or sub-oscillator G i . We can combine [(G 1 , G 2 )] in overlap (see Figure   32).
Note that the two IQuO-0 does not combine for generate an any IQuO normal (IQuO (n=1) ); then we could believe to the possibility of having a particular superposition of two sub-oscillators which origin a particular form of IQuO, defined IQuO-G. That is an (IQuO (n=1) ) with only one sub-oscillator.
This new possibility of combination in a superposition of IQuO-0 will be indicated with (⊕).
where the index 1-number indicates one state with only one sub-oscillator. The two matrices are equivalent. This configuration does not represents an IQuO but an overlap of two sub-oscillators in quantum entanglement (see the operation ⊕). We conjecture these possibilities as "Gluons". The possible combinations, with (⊕), of matrices are: One some representations (RB) can be ( Figure 34):

The Quarkcolor
The "massive coupling" builds the structure of couplings into quark ( Figure   35).
We conjecture that the sub-IQuO components of a quark have the same direction of phase rotation, because so quark is electrically charged. This vouches   Even with others configurations, for having a blue quark it needs that inside of it there is always any sub-oscillator with blue color (see Figure 38).
We have so a quark with blue color (Q B ). The index (B) is associated to in el a a + . Nevertheless, this configuration is possible if we introduce into primary chain a gluon-chain having the blue color, i.e. a blue-antired gluon: G BR .
Besides, recall into quark the sides to be built between a superposition of IQuO (see Figure 27), therefore the configuration of chain-sides (I BE + I CH ) could be ( Figure 39): The S-IQuO is the representative IQuO of a colored Quark (in this case the quark is blue). The representation matrix of three sub-oscillators is: The coupling between quark and a gluon could change the color of quark, i.
Another example: G. Guido

Conclusions
Talk about the physical properties as the electric charge, isospin, spin and color charge in some physics systems such as fields, it implies to add another freedom degree describing the corresponding phenomenon. We showed that all those properties can be connected to an internal freedom degree of the quantum oscillators representative of those fields. This shows that those systems are made of internal structures to associate with this internal freedom degree. Talking about internal structures in the system doesn't imply that it is composed by other parts linked or bounded together, but we could think instead that it is composed by coupled oscillators which establish a unique physical entity as an elementary particle. To introduce coupled oscillators system and geometrically structured we must think to peculiar quantum oscillators (IQuO) which internal freedom degree allows us to talk about those proprieties such as electric charge, isospin and color charge. The last one came from IQuO (n=2) and connected to the central sub-oscillator. In this way, the color charge states the existence of quantum oscillators represented by three sub-oscillators in which the energy is distributed with values of semi-quanta. Even, note that the gluons are not only inside quark as its components but they are go-between two quarks for build the hadrons. Recall the mesons. Mesons are hadrons composed of a quark-antiquark pair. The elementary mesons are pions. We conjectured [3] [4] the IQuO structure of Aureus triangles built by couplings between (u) and (d) quarks. If we recall the proton structure (see Figure 2), then we may build the form of the pion shown in Figure 41, where (u) is the u-antiquark.
The coupling between the u-quark and d-quarks results with quadrangular structure.
To link the two (u, d) quarks, it is necessary to add some junction IQuO between the sub-oscillators of the respective bases. The oscillators IQuO of the junction are the gluons. The "red" and "blue" colours of the sub-oscillators indicate the presence of descriptive coordinate: the "colour charge". The reciprocal phase shifts between G-IQuO and Q-IQuO of the quark structure must not dismantle the quark structure.