For examxple:. The photon is distinct from the boson Z 0 by virtue of its coupling with the electrical charge. The meaning of this physical quantity will be discussed in section Are elementary interactions a form of computation? For now we limit ourselves to remark that the electric charge Q of a given elementary fermion can be defined in terms of its biquaternion a , b.
If n is the number of color states of the internal edge associated with that fermion 1 for leptons, 3 for quarks , then the following relation holds:.
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The only possible action on internal edges leaving glyph topology and spatiotemporal explication of its elementary fermions unchanged is the permutation of the i , j , k axes. This permutation must be cyclic if the chirality of the triad has to be preserved.
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The leptons are changed in themselves by the transformation [ 1 , — 1 ], while the colors of the quarks inside a hadron will be exchanged while maintaining the total color white. For example the process:. The interaction quanta are in this case the gluons, mediators of the color interaction. As can be seen, they are very special quanta because unlike for example photons they do not propagate on spacetime between different interaction vertices.
Instead, they are directly exchanged between two quarks within a single vertex of strong interaction. These quarks can belong to the same hadron or to different hadrons with superposed de Sitter micro-spaces. Summarizing: the charge centers localized within a leptonic or hadronic microcosm, projected onto ordinary spacetime, are delocalized within this microcosm, more precisely within de Sitter's horizon of the tangent point-event O.
In the case of leptons, such delocalization can be assumed homogeneous given the absence of interactions with other centers of charge. Basically, a homogeneous phase plane wave can be assumed in the particle rest frame, which decays to null values beyond the horizon of O. In the hadron case there are several centers of charge that can interact with each other quarks and their spatial delocalization must therefore be described by appropriate internal orbitals of the particle. Two centers of charge can interact electromagnetically or through weak interaction, whether they belong to the same particle or to different particles.
In the hadronic case we must also consider the exchange of color between the quarks belonging to the same hadron or to different hadrons whose microuniverses have at least partially overlapping space-time projections. In this second case the interaction takes place in the overlapping region. The exchange of gluons is always virtual.
The spatial localization of a quantum in an interaction event is that of the charge centers coupled with the quantum in that event. So far we have talked of interactions involving individual elementary fermions. There are also interactions involving the physical particle lepton, hadron associated with the full glyph, seen as a whole. The first of these will be the merging of several hadrons and their subsequent dissociation in other hadrons. The more relevant distinction between the picture of hadronic processes presented in this paper and the current one is related to the relationship between a quark and the hadron it belongs to, which never is given up although the hadron itself can change , in any stage of interaction.
In fact, the glyph of a quark can only appear as a portion of a hadron glyph. The exchange of color color permutations between the quarks belonging to the same hadron can be described by introducing gauge quanta called gluons, but we must keep in mind that this exchange is always virtual: a gluon is emitted by a quark and absorbed by another quark of the same hadron. The gluons, therefore, never come out of the hadron microcosm in which they are exchanged they cannot be freely emitted or absorbed.
It is possible to have a gluonic exchange between quarks of different hadrons only if the projections, on ordinary spacetime, of their de Sitter microspaces admit a region of intersection; in this case the exchange can take place within this region. Naturally, even an exchange of this kind is virtual. The gluons therefore never appear as real particles asymptotic states.
The newly generated pair belongs to a neutral pion with its own de Sitter microspace, at least partially superposed to that of neutron. Subsequently, the neutral pion exchanges its own up quark with a down quark of the neutron turning into a negative pion. The neutron thus becomes a proton. The hadrodynamical interaction is thus intertwined with the color interaction in a way that preserves, at each instant, the belonging of a quark to a specific hadron.
The second interaction of this category is that gravitational, linked to the gauging of the four-momentum of the global physical particle lepton, hadron. We must note that the quadruplet [ 1 , i , j , k ] precedes, from a logical point of view, the emergence of spacetime and therefore cannot depend on the spacetime coordinates. However, Einstein taught us that it is possible to describe the gravitational field through an accessory metric. This metric defines a geometry in which the motion of an object in free fall in a gravitational field is described as free motion. From our point of view this means that it is necessary to generalize the Minkowski metric through the introduction of a connection, according to the criteria of general relativity.
The reasoning outlined in the previous section leads to a description of weak and strong interactions very similar to that offered by the Standard Model SM. In this section we expose in particular the connection to the electroweak sector of the SM Lagrangian.
We must first consider the situation in which the internal edges of the universal oscillator are defined in number and direction but its external edges are not. At this stage, the type of center of charge lepton, anti-lepton, quark, anti-quark is perfectly defined, but not its electric charge and weak isospin or the generation to which it belongs. Of course, the conclusions we come up to will be applicable to any other similar doublet, for example u,d. It is necessary to keep in mind that the single center of charge does not have a mass, because the mass is a feature of the particle understood as a whole de Sitter space with centers of charge inside it , not of the single center.
However, as we have seen in section Fragmentation of the void, the single center is located in the spacetime and therefore it is possible to define for it a wave function in effect, a second quantization operator depending on the spacetime coordinates. This topic has been dealt with in section Field operators, where field operators of centers of charge are shown to be fermionic.
One can assume, based on the topics at the end of that section, that all the centers of charge have spin 1 2 and this assumption is consistent with the experience. Fermions of spin 1 2 without mass are described by the equation:. This equation admits two distinct solutions, corresponding to two separate helicity states associated with the particle and the antiparticle respectively [ 12 ].
Since the type of center of charge quark or anti-quark, lepton or anti-lepton is defined, the helicity is also defined. It cannot be mutated by the electroweak interaction in itself, because this latter acts on the number and direction of the external edges of the universal oscillator, while the type of center of charge and hence the fermion helicity is defined by the direction of the internal edges.
The components of each doublet are coupled by an inversion of weak isospin, while singlets are coupled by neutral currents. The first two values are charge-conjugate, as the third and fifth and respectively the fourth and sixth are. We note that the right-hand doublet neutrino-electron and the left-hand doublet antineutrino-positron cannot exist, neither the components of a doublet can also appear as singlets. In these cases, indeed, the rule that associates a given helicity to a fermionic field respectively doublet or singlet and a helicity opposite to the corresponding anti-fermionic field would be violated.
The last interaction distinguishes electron by neutrino: only external edges entering the minor vertex are coupled, with a strength Q given by These bosons will be the following:. The iso-singlets of 30 can be coupled with themselves through A 3 and B. The gauge group of the electroweak interactions is therefore the direct product SU 2 x U 1 of the SU 2 group associated with weak interactions and the U 1 group associated with electromagnetic interactions.
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We omit the details of the construction, which can be found in every textbook on the subject here we conform to the notation of 13 ], but we underline that at this stage the gauge invariance is exact because there are no mass terms. In fact, we are talking about centers of charge, not particles. The Lagrangian at this point is the following:. The passage from the centers of charge to the particles involves the appearance of mass terms. The origin of these terms is a difficult topic that goes beyond the scope of this work. Note, however, that each center of charge is subject to a spatiotemporal localization within the particle to which it belongs, as we have seen in section Fragmentation of the void.
When an interaction occurs during which are created, annihilated or recombined in different particles virtual centers of charge, to be created or annihilated are always pairs of centers with opposite quantum numbers. The spatial and temporal scale of the appearance of these pairs is limited, in accordance with the uncertainty principle, and characterized by a finite Compton length for each center of charge. In Equation 31 additional terms must therefore appear that, suitably developed, generate the coupling terms of each center of charge with itself, with a coupling constant proportional to the reciprocal of the respective Compton length.
Of course, the appearance of these terms will destroy the gauge invariance. Instead, the hadron mass has not to be confused with the inverses in natural units of Compton lengths of constituent quarks.
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This field plausibly represents the state of the universal oscillator when the direction of the internal edge associated with the center of charge and hence the helicity, or the fact that the center is a fermion or an anti-fermion has not yet been defined. Coupling with the Higgs field is therefore a dynamic description of the adynamic definition of this direction in conjunction with an electroweak interaction.