Quarks :Frontiers in Elementary Particle Physics
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In Stock. Seller Inventory Book Description Condition: New. Seller Inventory S Book Description World Scientif. Seller Inventory BD Quarks: Frontiers in Elementary Particle Physics. Yoichiro Nambu. Here, he gives a first-person description of some of the main developments leading to our present view of the universe.
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Help Centre. Track My Order. My Wishlist Sign In Join. Be the first to write a review. Add to Wishlist. Ships in 7 to 10 business days. Link Either by signing into your account or linking your membership details before your order is placed. Description Product Details Click on the cover image above to read some pages of this book! Industry Reviews "Professor Nambu's book ia a useful addition to the library on elementary particles for the scientific layman. This energy scale is therefore greater than or equal to the reciprocal in natural units of the smaller Compton length that a center of charge can have.
Below the de Sitter radius corresponding to this length, de Sitter micro-universes corresponding to elementary particles are not formed, i. Thus, the Higgs field represents the mentioned state of the universal oscillator at every point in space time. This makes the role played by the Higgs field in the renormalization of the standard model understandable.
The signature of the 36 is the only one compatible with the existence of minima which differ from the vacuum. Now we can add to 31 both the term 35 and the interactions between the Higgs and the centers of charge:.
With the usual transformations the total Lagrangian thus obtained becomes that of SM. The latter takes the form:. The second term of 38 undergoes a similar transformation. In section Classification of elementary interactions it has been seen that weak interactions lead to a mixing of flavors. Mixing can be taken into account by repeating the previous reasoning for each of the leptonic doublet:. For what concerns the left-handed quarks, they form the doublets of weak isospin:.
Instead, right-handed quarks form singlets of weak isospin. The following relation then holds:.
Determining the mixing parameters remains an open problem. It is necessary to consider that so far this field has been studied in the context of the unitary evolution of field operators. But, to our knowledge, no inquiry has ever been made about the relationship between the Higgs field and the discontinuities of that evolution, namely the quantum jumps QJ. Let's now explain the symbols.
Quarks: Frontiers in Elementary Particle Physics
The parameter T is connected to the particle mass M through the relation:. Let us now look at the physical meaning of the hypothesis. The interested reader can consult Chiatti [ 18 ] for a possible theoretical justification of these tails. This field manifests itself when a massive particle undergoes a quantum jump. Operating with the energy operator on 44 and on 45 respectively we find:. They are imaginary, and thus define the line width of a transient consisting of the particle that contains the centers of charge.
This result conforms to the notion of particles as events rather than objects. In other words, this description seems to correspond approximately to QFT after performing the renormalization procedure, with the consequent subtraction of free propagation diagrams. As can be seen, the coupling described by 44 , 45 represents at the same time: 1 the localization of the particle in the temporal domain; 2 the self-interaction of the particle induced by its real interaction with the external world the same that, inter alia , causes the QJ ; 3 the coupling of the centers of charge inside the particle with the Higgs field.
In the case of particles containing a single center of charge leptons the coupling constant with the Higgs field, multiplied by the expectation value in the vacuum of this latter, is the mass of the particle while the time constant T of 44 , 45 is the reciprocal of that mass. In the case of quarks, the first quantity is the reciprocal in natural units of the Compton length of the quark while T , which is the same for all quarks of the same hadron, is the reciprocal of the hadron mass. The asymptotic state can also contain virtual interactions, such as in the case of an electron in a stationary atomic orbital, which exchanges virtual photons with the nucleus.
At this point we can come back to the initial question of this section, that is, the true nature of the Higgs field. The Higgs field exists because there are fluctuations in the vacuum corresponding to the state of the universal oscillator with undefined orientation of the internal edge and suppressing these fluctuations costs energy. The centers of charge inside a particle are coupled, in the time neighborhood of a QJ, with this fluctuations field.
The coupling energy is given by the product of the coupling constant for the expectation value of the Higgs field in the vacuum. This product is the reciprocal of the Compton length of the center of charge. This actualization is the creation of the charges; the decay constant of this process is the reciprocal of the mass of the particle. When an energy equal to that of coupling between the centers of charge inside a particle and the expectation value of the Higgs field is made available in the QJ, that particle may appear as a virtual transient phenomenon; its actual creation requires that energy equal to the mass of the particle is available.
It is also noteworthy that the quark top does not form hadrons, which support the hypothesis that it is placed precisely at the extreme limit beyond which the particle formation is no longer possible or very difficult. In this section we intend to explain, before going on to the conclusions, some reflections on the role played by the algebraic structures in the present approach.
To our best knowledge, the peculiarity of this role distinguishes our proposal from other algebraic models, available in literature, also aimed at the theoretical justification of the Standard Model. In particular we want to briefly discuss some correspondences and differences with the recent and fascinating works of Furey [ 19 , 20 , 21 , 22 ] and Stoica [ 23 ].
It is first necessary to consider that the questions explicitly formulated by both these authors as motivations for their research are the same ones that we have set ourselves and which we have illustrated in the introductory part of this work. These questions can be summarized in one: is there a general theoretical principle that explains why the elementary particles that we see in nature are those that are, and interact with the modalities we actually observe? Furey and Stoica both answer affirmatively, as we do. Like us, even these authors hypothesize the existence of an algebraic constraint that selects the field operators of the Standard Model.
The identification of this constraint thus becomes the fundamental goal of the research. While these intentions are common to the two approaches ours and those of these authors , an important difference must be found in the understanding of the constraint. Furey and Stoica assume that the Standard Model can be formulated in terms of a Clifford algebra on a numerical field representative of a division algebra real numbers, complex numbers, quaternions or octonions or on direct products of such fields.
The operators of the Standard Model then become elements of this Clifford algebra, more precisely ideals, and this fact represents the constraint sought. Both Furey and Stoica show that a complex Clifford algebra Cl 6 can accommodate a single generation of elementary fermions quarks and leptons of the Standard Model.
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Furey goes further, succeeding in demonstrating: 1 that the ideals of an algebraic structure built on the chains of multiplications between octonions can be put in correspondence with the three generations of elementary fermions [ 21 ]; 2 that the ideals of a complex quaternionic algebra can be put in correspondence both with Dirac spinors and with spacetime quadrivectors [ 19 , 22 ]. One may ask what is the physical reason which privileges such algebraic structures. Field operators are used to describe interactions, so it seems plausible that logical constraints on their algebra derive from the nature of interactions.
In this regard Furey makes interesting considerations [ 19 ]. Her proposal is to interpret interactions as algebraic operations, emphasizing how both are irreversible. There is no way to uniquely return to the addends 3 and 2 from the result 5 of their sum, as there is no way to restore the wave function immediately after its collapse. The physical world, understood as a network of interaction events, is then a locally limited graph provided with a partial order relation, i. The nodes of this graph are operations and the flow on the graph takes place in accordance with the rules of a specific algebra.
Our idea is similar, in the sense that the vertices of interaction are our starting point. However, there are three important differences compared to the Furey proposal:. Our algebraic structure constitutes an aspatial and timeless background, which connects to the spatio-temporal domain in discrete events that are the vertices of interaction.
Real interactions are considered here, corresponding to the collapse of the quantum wave function.
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The interactions therefore have a double dynamic role due to their influence on the unitary evolution of the wave function and adynamic collapse. The particles come out of this condition, or return into it, in conjunction with an interaction.
This difference between the starting points of our work and those of Furey and Stoica immediately leads to a difference in formalism. The algebraic structure considered in section Directed glyphs and hypercomplex numbers for the description of matter is in fact constituted by biquaternionic units, not by quaternions in a general sense. No multiplication of these units for a real number is defined, nor any addition operation we only use the weaker notion of cancellation of opposite units in section Conclusions.
The considered algebraic structure is therefore drastically simpler than those examined by Furey and Stoica, because no numerical field is present. Their relations remain the same regardless of the choice of the arrangement of the triad of vertices on the sphere, and the value of the spherical radius. This allows the definition of a spatio-temporal order co-emergent with the matter section Fragmentation of the void. To each particle involved in a real interaction event, described in quantum mechanics by the collapse of the wave function, corresponds to a succession of algebraic operations that leads to the spatio-temporal manifestation of that particle, with its centers of charge.
These centers are the elementary fermions of the Standard Model.
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These operations, carried out in succession, cause the universal oscillator to pass from the symmetrical vacuum state to that corresponding to the specific elementary particle. Quantum amplitudes can be associated with these transitions section Field operators , which are connected to a vacuum state through Fock operators and it is only at this stage that the addition appears as requested by the superposition principle.
Superpositions of amplitudes can be used to represent the quantum amplitude of the process before or after collapse. It is the classification of field operators obtained in this way that can be compared with those derived from other approaches.
In other words, the symmetry breaking associated with the collapse of the wave function occurs at a level that is not that of QFT and it leads to the base states of the QFT description; it is only at this point that the superposition of these latter is introduced, corresponding to the quantum second quantization amplitude of the QFT description. This is a different procedure from the usual one consisting in starting with a QFT state provided with a certain symmetry and then selecting base states from a process, also inside the QFT, of symmetry breaking.