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E-grāmata: Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation

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, (Thechnical University Gh.Asachi Iasi, Romania),
  • Formāts: 256 pages
  • Izdošanas datums: 12-Sep-2019
  • Izdevniecība: CRC Press
  • Valoda: eng
  • ISBN-13: 9781000751260
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Mathematical Principles of Scale Relativity Physics: The Concept of InterpretationPalielināt
  • Formāts: 256 pages
  • Izdošanas datums: 12-Sep-2019
  • Izdevniecība: CRC Press
  • Valoda: eng
  • ISBN-13: 9781000751260
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This book explores and builds upon the principles of Laurent Nottale’s scale relativity. It provides a unified framework for the treatment of a number of problems encountered by researchers studying the dynamics of physical systems. The work will be of interest to graduate students and academic researchers working in mathematics and physics.

The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation

explores and builds upon the principles of Laurent Nottale’s scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale’s scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics.

Key Features:

  • Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics

  • Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom

  • Establishes a natural connection between the Newtonian forces and the Planck’s law from the point of view of space and time scale transition: both are expressions of invariance to scale transition

The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.

Chapter 1 Introduction
4(14)
Chapter 2 Madelung Fluid Dynamics
18(26)
The Madelung Fluid
19(6)
Classical and Quantum Conservation Laws
25(4)
Hydrodynamics of Free Point Particles: Universality of the Schrodinger Equation
29(3)
A Definition of the Interpretation
32(12)
Chapter 3 De Broglie's Interpretation of Wave Function
44(16)
The Appropriate Geometry of de Broglie's Idea
52(3)
Lessons and Mandatory Developments
55(5)
Chapter 4 The Planetary Model as a Dynamical Kepler Problem
60(16)
A Newtonian Brief on Density
69(2)
The Concept of Confinement
71(3)
A Clasic Example of Affine Reference Frame: Maxwell Stress Tensor
74(2)
Chapter 5 The Light in a Schrodinger Apprenticeship
76(10)
A Special Contribution of Helmholtz
79(4)
Enters Erwin Schrodinger
83(3)
Chapter 6 The Wave Theory of Geometric Phase
86(24)
Enters Sir Michael Berry
86(5)
A Kepler Motion Analysis: the Geometrical Condition of Yang-Mills Fields
91(5)
The Berry Moment of Human Knowledge
96(5)
A Classical Implementation of the Idea of Interpretation
101(4)
A Characterization of the Hertz's Material Point
105(2)
The General Meaning of Berry's Curvature
107(3)
Chapter 7 The Physical Point of View in the Theory of Surfaces
110(22)
A Few Mathematical Prerequisites
110(4)
The Differential Theory of Surfaces
114(4)
Rainich's Description of Surrounding Space
118(3)
A Physical Parametrization of Surface
121(3)
The Three-Dimensional Space of Accelerations
124(4)
Force at an Outward Distance
128(4)
Chapter 8 Nonconstant Curvature
132(18)
The Infinitesimal Deformation
134(4)
Summing up the Differential Geometry of Curvature Parameters
138(1)
A Definition of Surface Tension
139(3)
The Statistics of Fluxes on a Material Point
142(3)
The Stress by a Statistic
145(2)
The Tensions: Conclusions and Outlook
147(3)
Chapter 9 The Nonstationary Description of Matter
150(16)
The Louis de Broglie Moment
150(4)
Airy Moment of Berry and Balazs
154(7)
Cosmological Moment of Berry and Klein
161(5)
Chapter 10 The Idea of Continuity in Fluid Dynamics
166(18)
The Mass Transport in a Volume Element
166(4)
The Transport Theorem in Finite Volume
170(3)
Some Classic Physical Examples
173(3)
The Hamiltonian Transport in Finite Volume
176(2)
Transcendence between Volume Element and a Control Volume
178(6)
Chapter 11 A Hertz-type Labelling in a Madelung Fluid
184(24)
Torsion Induced by Space Variations of Density
196(2)
The Reference Frame and the Torsion
198(3)
The Torsion and the Waves
201(7)
Chapter 12 Theory of Nikolai Alexandrovich Chernikov
208(13)
Enters Chernikov
209(7)
Chernikov's Theory in the Three-Dimensional Case
216(5)
Conclusions: Concept of Interpretation and Necessary Further Elaborations 221(10)
References 231(18)
Subject Index 249
Nicolae Mazilu is a researcher at the Institute of Nuclear Research, Romania, an associate researcher at the University of Akron, USA, and recently retired as a Senior Project Engineer at Bridgestone/Firestone, Inc., USA; Maricel Agop is an associate researcher at the Technical University Gheorghe Asachi and Al.I.Cuza University, Romania: Ioan Merches is Professor Emeritus, at Al.I.Cuza University, Iasi, Romania.
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