scholarly journals The Nakano–Nishijima–Gell-Mann Formula from Discrete Galois Fields

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1603
Author(s):  
Keiji Nakatsugawa ◽  
Motoo Ohaga ◽  
Toshiyuki Fujii ◽  
Toyoki Matsuyama ◽  
Satoshi Tanda
Keyword(s):  
Group Theory ◽  
Gauge Invariance ◽  
Lorentz Invariance ◽  
Galois Field ◽  
Elementary Particles ◽  
Composite Particles ◽  
Real Numbers ◽  
Quark Confinement ◽  
Charge Number ◽  
Quantum Numbers

The well known Nakano–Nishijima–Gell-Mann (NNG) formula relates certain quantum numbers of elementary particles to their charge number. This equation, which phenomenologically introduces the quantum numbers Iz (isospin), S (strangeness), etc., is constructed using group theory with real numbers R. But, using a discrete Galois field Fp instead of R and assuring the fundamental invariance laws such as unitarity, Lorentz invariance, and gauge invariance, we derive the NNG formula deductively from Meson (two quarks) and Baryon (three quarks) representations in a unified way. Moreover, we show that quark confinement ascribes to the inevitable fractionality caused by coprimeness between half-integer (1/2) of isospin and number of composite particles (e.g., three).

scholarly journals Normalizability analysis of the generalized quantum electrodynamics from the causal point of view

2017 ◽  
Vol 32 (27) ◽  
pp. 1750165 ◽  
Author(s):  
R. Bufalo ◽  
B. M. Pimentel ◽  
D. E. Soto
Keyword(s):  
Perturbation Theory ◽  
Physical Model ◽  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Lorentz Invariance ◽  
Point Of View ◽  
Inductive Method ◽  
S Matrix ◽  
Causal Approach

The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyze the implication of the gauge invariance onto the model and obtain the respective Ward–Takahashi–Fradkin identities.

A Problem of Mass

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Long Range ◽  
Gauge Invariance ◽  
Weak Interactions ◽  
Elementary Particles ◽  
Gauge Invariant ◽  
Zero Mass ◽  
Gauge Symmetries ◽  
Symmetry Properties ◽  
Long Range Interactions ◽  
The Masses

This chapter examines the constraints coming from the symmetry properties of the fundamental interactions on the possible values of the masses of elementary particles. We first establish a relation between the range of an interaction and the mass of the particle which mediates it. This relation implies, in particular, that long-range interactions are mediated by massless particles. Then we argue that gauge invariant interactions are long ranged and, therefore, the associated gauge particles must have zero mass. Second, we look at the properties of the constituents of matter, the quarks and the leptons. We introduce the notion of chirality and we show that the known properties of weak interactions, combined with the requirement of gauge invariance, force these particles also to be massless. The conclusion is that gauge symmetries appear to be incompatible with massive elementary particles, in obvious contradiction with experiment. This is the problem of mass.

Integral powers of order three Latin square matrices

2009 ◽  
Vol 93 (526) ◽  
pp. 42-50 ◽  
Author(s):  
N. Gauthier
Keyword(s):  
Group Theory ◽  
Permutation Group ◽  
Matrix Theory ◽  
Latin Square ◽  
Latin Squares ◽  
Classroom Discussions ◽  
Real Numbers ◽  
Permutation Matrices ◽  
The Matrix

An order-n Latin square contains numbers, each of which is one of a set of n real numbers, , arranged in the form of an n × n matrix, in such a way that each row and each column of the matrix contains all n numbers. Euler (1707-1783) was the first to study the properties of Latin squares and they have been the focus of continued attention since. Studies of Latin squares naturally lead one to elements of group theory and of matrix theory. As will be shown in this note, both of these features may offer interesting investigative opportunities for classroom discussions of the permutation group on three symbols and of the algebra of the associated permutation matrices.

scholarly journals The SLq(2) extension of the standard model

2015 ◽  
Vol 30 (16) ◽  
pp. 1530037 ◽  
Author(s):  
Robert J. Finkelstein
Keyword(s):  
Composite Structure ◽  
Elementary Particles ◽  
Present Form ◽  
Composite Particles ◽  
Lagrangian Dynamics ◽  
Fundamental Representation ◽  
Current Form ◽  
The Standard Model ◽  
Small Set ◽  
Original Picture

The idea that the elementary particles might have the symmetry of knots has had a long history. In any modern formulation of this idea, however, the knot must be quantized. The present review is a summary of a small set of papers that began as an attempt to correlate the properties of quantized knots with empirical properties of the elementary particles. As the ideas behind these papers have developed over a number of years, the model has evolved, and this review is intended to present the model in its current form. The original picture of an elementary fermion as a solitonic knot of field, described by the trefoil representation of SUq(2), has expanded into its present form in which a knotted field is complementary to a composite structure composed of three preons that in turn are described by the fundamental representation of SLq(2). Higher representations of SLq(2) are interpreted as describing composite particles composed of three or more preons bound by a knotted field. This preon model unexpectedly agrees in important detail with the Harari–Shupe model. There is an associated Lagrangian dynamics capable in principle of describing the interactions and masses of the particles generated by the model.

scholarly journals GAUGE INVARIANCE AND THE GOLDSTONE THEOREM

2011 ◽  
Vol 26 (19) ◽  
pp. 1381-1392 ◽  
Author(s):  
GERALD S. GURALNIK
Keyword(s):  
Gauge Invariance ◽  
Gauge Theories ◽  
Elementary Particles ◽  
Max Planck ◽  
Goldstone Theorem ◽  
Zero Mass ◽  
Unified Theories

This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.

scholarly journals A theory of particle physics about quantum number constrained equation and particle singularity

2020 ◽  
Author(s):  
Ma Hua
Keyword(s):  
Quantum Number ◽  
Particle Physics ◽  
Composite Particle ◽  
Great Influence ◽  
Symmetry Transformation ◽  
Composite Particles ◽  
Transformation Mechanism ◽  
Quantum Numbers ◽  
Constrained Equation ◽  
Good Agreement

Abstract In this paper, two fundamental problems of particle physics are studied theoretically. The first one is: to solve the problem of establishing general quantum number constrained equation, the symmetry transformation mechanism of charge eigenstates for elementary particles is adopted, and the quantum number constrained equation is established, which is applicable to physical particles. For hadrons, this equation is completely consistent with Gell-Mann-Nishijima formula. For leptons, the lepton quantum numbers are exactly the solutions of this equation. The second one is: to solve the problem of understanding singularity and calculating singular numbers, a hypothesis that a composite particle may has virtual structure is proposed. According to this hypothesis, the singular particles must be composite particles, and have virtual structures. In a virtual structure, the particles and antiparticles of component particles can form particle-antiparticle pairs, which have great influence such as improving mass and changing life of composite particles. Therefore, the composite particle with particle-antiparticle pairs in its virtual structure is singular particle, and the singular number is the number of particle-antiparticle pairs. These two theoretical results are in good agreement with the already achieved experimental results of particle physics, can explain the related phenomena of physical particles from a deeper physical mechanism, and theoretically predict the existence of singular leptons and several new singular hadrons.

scholarly journals Tests of the CPT Invariance at the Antiproton Decelerator of CERN

2019 ◽  
Vol 64 (7) ◽  
pp. 589
Author(s):  
D. Horváth
Keyword(s):  
Cosmic Rays ◽  
Standard Model ◽  
Gauge Invariance ◽  
Particle Physics ◽  
Composite Particles ◽  
Cpt Invariance ◽  
Invariance Principles ◽  
Antiproton Decelerator ◽  
The Standard Model ◽  
Cp Symmetry

The Standard Model, the theory of particle physics is based on symmetries: both the structure of the composite particles and their interactions are derived using gauge invariance principles. Some of these are violated by the weak interaction like parity and CP symmetry, and even masses are created via spontaneous symmetry breaking. CPT invariance, the most essential symmetry of the Standard Model, states the equivalency of matter and antimatter. However, because of the lack of antimatter in our Universe it is continuously tested at CERN. We overview these experiments: measuring the properties of antiprotons as compared to those of the proton at the Antiproton Decelerator and also searching for antimatter in cosmic rays.

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