Knots, Braids And Mobius Strips - Particle Physics And The Geometry Of Elementarity: An Alternative View

by Jack Shulman Avrin

Overview

Elementary particles in this book exist as Solitons in-and-of the fabric of spacetime itself. As such they are characterized by their geometry, that is their topology and configuration which lead directly to their physical attributes and behavior as well as to a simplification and reduction of assumptions and the importation of parameter values. The emphasis of the book is thus on that geometry, the algebraic geometry associated with taxonomical issues and the differential geometry that determines the physics as well as on simplifying the results. In itself, however, the process of assembling and developing what eventually went into the book has been a singularly rewarding journey. Along the way some fascinating insights and connections to known physical attributes and theories emerge, some predictable but others unbidden and even unanticipated. The book is intended to summarize that journey in a way that, readers with a range of backgrounds will find interesting and provocative. Connections to other physical theories and subjects are also discussed. A most gratifying development is the emergence of a unifying principle underlying the epistemological structure of not only the elementary particles but of such diverse fields as Radar, Quantum mechanics, Biology, Cosmology and the Philosophy of science.

Product Details

ISBN-13:	9789814616003
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	04/29/2015
Series:	Series On Knots And Everything , #55
Pages:	356
Product dimensions:	6.30(w) x 9.00(h) x 0.90(d)

Table of Contents

Acknowledgments vii

Preface xiii

I Introduction: Some History and Philosophy 1

1 History and Philosophy 3

II Basic Concepts: Algebraic Geometry 19

2 Genesis of a Particle Model 21

3 First-Order Fusion 41

4 Dirac and Traverse 47

5 Second-Order Fusion 51

6 Combinatorial Perspective (Analysis) 57

7 More Perspective 60

8 Composition and Contingency 65

III Algebraic Ruminations 75

9 The Bialgebra and Hopf Algebra Connection 77

10 A Foray into Quantum Mechanics 85

11 Spin, Spinors, and the Pauli Connection 91

12 Magnetic Moments 98

13 Quaternions 101

14 A Variant of the Bracket for (2, n) Torus Knots 107

IV The Standard Model Connection 113

15 Ambiguities and Direct Comparison 115

16 Some Interactions: Delta Creation and Decay 118

17 Beta Decay 122

18 "Deuteronomy" and Isospin Invariance 127

19 Simple Symmetry and CPT Invariance 130

20 Family Matters 134

V Basic Concepts: Differential Geometry 145

21 Preliminaries 147

22 Solitonic Behavior; The Geodetic Approach 162

23 The Lagrangian Approach 166

24 Solitonic Antiparticles 170

25 Particle Parameters: Mass and Size 173

26 Mass, the Higgs and the Strong Force 176

27 A Parallel to the Higgs 179

28 The Central "Entity" 187

29 A Constraint 191

30 Postscript: Spinoza. Clifford, Einstein. Wheeler and Me 195

VI Assorted Topics, Some Speculative 199

31 Time: CPT, Instantons and Triplication 201

32 Dark Matter 213

33 TQFT 218

34 The String Theory Connection 224

35 Another sine Gordon System 226

VII Perspective 231

36 Recapitulation 233

37 Cosmology, Beta Decay and Anthropic Matters 240

38 Herpetological Closure 247

39 The Universe and the Marketplace 255

40 The Alternative Model and Quantization 259

41 Quantum Gravity? 263

42 Conclusions 270

43 Supplementary Conclusions 275

44 Postscript 284

Appendices 287

Appendix A Illustrating the Double Traversal Requirement 289

Appendix B Torus Knot Connection Terms 290

Appendix C Curvature for the Lagrangian 292

Appendix D Contingency in Second Order Fusion 294

Appendix E The Beta Switch 298

Appendix F The Alternative Model, DNA and Dark Matter Redux 300

References 315

Index 319