ابعاد ۸×۲n ذرات: از مکانیک سازه‌ای تا فیزیک ذرات از طریق ریاضیات اوکتونیون

The properties of elementary particles, which determine the interactions between them, must result from the form and function of their internal structure. This investigation stems from the mathematical origin of the concept of particles and the introduction to the process of octal decomposition. It is then established that in order for the complete and specific identification of the dynamic and kinematic characteristics of the function of their internal structures, particles must be defined by a system of 16 dimensions, consisting of two subsystems of eight dimensions. Table of Contents PREFACE INTRODlTCTION OVERVIEW 1. Octonion Mathematics for Physics 2. The Deformable Continuum 3. The Particle 4. One-dimensional Aggregates of Two-di mentional Particles 5. Two-dimensional Aggregates of One-dimensional Particles 6. Three-dimensional Aggregates of Particles 1. OCTONIONS 1.1 OCTONION ALGEBRA 1.1.1 Linear Algebras without Divisors of Zero (LAwDoZ) 1.1.2 Octonion Product 1.1.3 Octonion Tensors 1.1.4 Polar and Axial Vectors 1.1.5 Orthogonal Transformations 1.1.6 Position Vectors 1.1.7 Position Vectors 1.1.8 Free Polar Vectors 1.1.9 The Polar Position 1.1.10 Orientation Vectors 1.2 OCTONION ANALYSIS 1.2.1 Octonion Functions 1.2.2 Partial derivatives 1.2.3 Derivatives with respect to an octonion 1.2.4 Extend Cauchy - Riemann Equations 1.2.5 Octonion Potential Functions 1.2.6 Octonion Line Integrals 1.2.7 Extended Cauchy's Integral Theorem 1.2.8 Extended Cauchy's Integral Formula 1.2.9 Formulas of Gauss, Stokes and Green 2. THE DEFORMABLE CONTINUUM 2.1. The Concept of the Deformable Continuum 2.2. Translations and Strains 2.3 Orbital Velocities and Strain Rates 2.4 Forces and Stresses 2.5 Orbital Momentums and Impulses 2.6 Constitutive Laws of Solids 2.7 Constitutive Laws of Liquids 2.8 Constitutive Laws of Gauges 2.9 A Vacuum Hypothesis 3. THE PARTICLE 3.1 The Concept of Particle 3.2 Motives, Composants, Shape and Lever-arm Functions 3.3 Invariants 3.4 Conformal and Contra-formal Motions 3.5 The Octal Decomposition 3.6 Polar Vector Composants and Motives 3.7 Axial Vector Composants and Motives 3.8 Induction Moments 3.9 Real Scalar Composants and Motives 3.10 Imaginary Scalar Composants and Motives 3.11 Spin and Bi-moment 3.12 The Complete System of Composants and Motives 4. ONE-DIMENSIONAL AGGREGATES OF TWO-DIMENSIONAL PARTICLES 4.1 Beams and String 4.2 Reference Systems 4.3 The Bi-quaternal Decomposition 4.4 Lateral Force Composants and Motives 4.4.1 Polar Vector Composants and Motives 4.4.2 Axial Vector Composants and Motives 4.4.3 Real Scalar Composants and Motives 4.5 Normal Force Composants and Motives 4.5.1 Polar Vector Composants and Motives 4.5.2 Axial Vector Composants and Motives 4.5.3 Imaginary Scalar Composanls and Motives 4.5.4 Contra-formal Normal Composauts and Motives 4.6 The Complete System of State Parameters 4.7 Loads and Stresses 4.8 Interacting Composants 4.8.1 Normal Interacting Composants 4.8.2 Lateral Interacting Composants 4.9 Hidden Composants 4.9.1 Normal Hidden Composants 4.9.2 Lateral Hidden Composants 4.9.3 Universal Strains and Stresses 5. TWO DIMENSIONAL AGGREGATES OF DIMENSIONAL PARTICLES 5.1 Surface Systems 5.2 Reference System 5.3 The Tri-Dual Decomposition 5.4 Loads and Stresses 5.5 Interacting Composants 5.6 Hidden Cornposants 5.7 Inter-composant Relations 5.7.1 Inter-tangential Composants Relations 5.7.2 Axial to Polar Vector Composants Relations 5.7.3 Polar Vector Composants to Loads Relations 5.7.4 Real Scalar lnteracting to Hidden Composants Relation 5.8 Motives 5.9 Universal Strains and Stresses 6. THREE-DIMENSIONAL AGGREGATES OF PARTICLES 6.1 Zero-Dimensional Particles 6.2 Solid Particles of Finite Size 6.3 Solid Particles of Infinite Size About the author