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Physics from Symmetry Second Edition 2018 [Kietas viršelis]

4.64/5 (42 ratings by Goodreads)

Jakob Schwichtenberg

Formatas: Hardback, 287 pages, aukštis x plotis: 279x210 mm, 15 Illustrations, color; 13 Illustrations, black and white; XXI, 287 p. 28 illus., 15 illus. in color., 1 Hardback
Serija: Undergraduate Lecture Notes in Physics
Išleidimo metai: 18-Dec-2017
Leidėjas: Springer International Publishing AG
ISBN-10: 3319666304
ISBN-13: 9783319666303

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Mathematical physics - (Šiuo metu turimos knygos: 1 prekės)
Particle & high-energy physics - (Šiuo metu turimos knygos: 1 prekės)
Groups & group theory

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Formatas: Hardback, 287 pages, aukštis x plotis: 279x210 mm, 15 Illustrations, color; 13 Illustrations, black and white; XXI, 287 p. 28 illus., 15 illus. in color., 1 Hardback
Serija: Undergraduate Lecture Notes in Physics
Išleidimo metai: 18-Dec-2017
Leidėjas: Springer International Publishing AG
ISBN-10: 3319666304
ISBN-13: 9783319666303

Kitos knygos pagal šią temą:

Mathematical physics - (Šiuo metu turimos knygos: 1 prekės)
Particle & high-energy physics - (Šiuo metu turimos knygos: 1 prekės)
Groups & group theory

Pastovi nuoroda: https://www.kriso.lt/db/9783319666303.html

This is a textbook that derives the fundamental theories of physics from symmetry.
It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived.

As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.

Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.

Part I Foundations

1 Introduction

(8)

1.1 What we Cannot Derive

(2)

1.2 Book Overview

(2)

1.3 Elementary Particles and Fundamental Forces

(4)

2 Special Relativity

(14)

2.1 The Invariant of Special Relativity

(2)

2.2 Proper Time

(2)

2.3 Upper Speed Limit

(1)

2.4 The Minkowski Notation

(2)

2.5 Lorentz Transformations

(2)

2.6 Invariance, Symmetry and Covariance

(4)

Part II Symmetry Tools

3 Lie Group Theory

(70)

3.1 Groups

(3)

3.2 Rotations in two Dimensions

(4)

3.2.1 Rotations with Unit Complex Numbers

(2)

3.3 Rotations in three Dimensions

(5)

3.3.1 Quaternions

(4)

3.4 Lie Algebras

(12)

3.4.1 The Generators and Lie Algebra of SO(3)

(3)

3.4.2 The Abstract Definition of a Lie Algebra

(1)

3.4.3 The Generators and Lie Algebra of SU(2)

(1)

3.4.4 The Abstract Definition of a Lie Group

(3)

3.5 Representation Theory

(4)

3.6 SU(2)

(8)

3.6.1 The Finite-dimensional Irreducible Representations of SU(2)

(7)

3.6.2 The Representation of SU(2) in one Dimension

(1)

3.6.3 The Representation of SU(2) in two Dimensions

(1)

3.6.4 The Representation of SU(2) in three Dimensions

(1)

3.7 The Lorentz Group O(1, 3)

(27)

3.7.1 One Representation of the Lorentz Group

(3)

3.7.2 Generators of the Other Components of the Lorentz Group

(1)

3.7.3 The Lie Algebra of the Proper Orthochronous Lorentz Group

(2)

3.7.4 The (0, 0) Representation

(1)

3.7.5 The (1/2, 0) Representation

(2)

3.7.6 The (0, 1/2) Representation

(1)

3.7.7 Van der Waerden Notation

(5)

3.7.8 The (1/2, 1/2) Representation

(4)

3.7.9 Spinors and Parity

(2)

3.7.10 Spinors and Charge Conjugation

(1)

3.7.11 Infinite-Dimensional Representations

(2)

3.8 The Poincare Group

(2)

3.9 Elementary Particles

(1)

3.10 Appendix: Rotations in a Complex Vector Space

(1)

3.11 Appendix: Manifolds

(2)

4 The Framework

(22)

4.1 Lagrangian Formalism

(2)

4.1.1 Fermat's Principle

(1)

4.1.2 Variational Calculus -- the Basic Idea

(1)

4.2 Restrictions

(1)

4.3 Particle Theories vs. Field Theories

(1)

4.4 Euler-Lagrange Equation

(2)

4.5 Noether's Theorem

101

(12)

4.5.1 Noether's Theorem for Particle Theories

101

(4)

4.5.2 Noether's Theorem for Field Theories -- Spacetime Symmetries

105

(3)

4.5.3 Rotations and Boosts

108

(2)

4.5.4 Spin

110

(1)

4.5.5 Noether's Theorem for Field Theories -- Internal Symmetries

110

(3)

4.6 Appendix: Conserved Quantity from Boost Invariance for Particle Theories

113

(1)

4.7 Appendix: Conserved Quantity from Boost Invariance for Field Theories

114

(3)

Part III The Equations of Nature

5 Measuring Nature

117

(4)

5.1 The Operators of Quantum Mechanics

117

(2)

5.1.1 Spin and Angular Momentum

118

(1)

5.2 The Operators of Quantum Field Theory

119

(2)

6 Free Theory

121

(10)

6.1 Lorentz Covariance and Invariance

121

(1)

6.2 Klein-Gordon Equation

122

(2)

6.2.1 Complex Klein-Gordon Field

124

(1)

6.3 Dirac Equation

124

(3)

6.4 Proca Equation

127

(4)

7 Interaction Theory

131

(46)

7.1 U(1) Interactions

133

(10)

7.1.1 Internal Symmetry of Free Spin 1/2 Fields

134

(1)

7.1.2 Internal Symmetry of Free Spin 1 Fields

135

(1)

7.1.3 Putting the Puzzle Pieces Together

136

(3)

7.1.4 Inhomogeneous Maxwell Equations and Minimal Coupling

139

(1)

7.1.5 Charge Conjugation, Again

140

(1)

7.1.6 Noether's Theorem for Internal U(1) Symmetry

141

(1)

7.1.7 Interaction of Massive Spin 0 Fields

142

(1)

7.1.8 Interaction of Massive Spin 1 Fields

143

(1)

7.2 SU(2) Interactions

143

(7)

7.3 Mass Terms and "Unification" of SU(2) and U(1)

150

(8)

7.4 Parity Violation

158

(4)

7.5 Lepton Mass Terms

162

(3)

7.6 Quark Mass Terms

165

(1)

7.7 Isospin

166

(4)

7.7.1 Labelling States

168

(2)

7.8 U(3) Interactions

170

(4)

7.8.1 Color

172

(1)

7.8.2 Quark Description

173

(1)

7.9 The Interplay Between Fermions and Bosons

174

(3)

Part IV Applications

8 Quantum Mechanics

177

(32)

8.1 Particle Theory Identifications

178

(1)

8.2 Relativistic Energy-Momentum Relation

178

(1)

8.3 The Quantum Formalism

179

(3)

8.3.1 Expectation Value

181

(1)

8.4 The Schrodinger Equation

182

(3)

8.4.1 Schrodinger Equation with an External Field

185

(1)

8.5 From Wave Equations to Particle Motion

185

(11)

8.5.1 Example: Free Particle

185

(1)

8.5.2 Example: Particle in a Box

186

(3)

8.5.3 Dirac Notation

189

(2)

8.5.4 Example: Particle in a Box, Again

191

(1)

8.5.5 Spin

192

(4)

8.6 Heisenberg's Uncertainty Principle

196

(1)

8.7 Comments on Interpretations

197

(1)

8.8 Appendix: Interpretation of the Dirac Spinor Components

198

(5)

8.9 Appendix: Solving the Dirac Equation

203

(2)

8.10 Appendix: Dirac Spinors in Different Bases

205

(4)

8.10.1 Solutions of the Dirac Equation in the Mass Basis

207

(2)

9 Quantum Field Theory

209

(24)

9.1 Field Theory Identifications

210

(1)

9.2 Free Spin 0 Field Theory

211

(5)

9.3 Free Spin 1/2 Field Theory

216

(3)

9.4 Free Spin 1 Field Theory

219

(1)

9.5 Interacting Field Theory

219

(10)

9.5.1 Scatter Amplitudes

220

(1)

9.5.2 Time Evolution of States

220

(4)

9.5.3 Dyson Series

224

(1)

9.5.4 Evaluating the Series

225

(4)

9.6 Appendix: Most General Solution of the Klein-Gordon Equation

229

(4)

10 Classical Mechanics

233

(6)

10.1 Relativistic Mechanics

235

(1)

10.2 The Lagrangian of Non-Relativistic Mechanics

236

(3)

11 Electrodynamics

239

(6)

11.1 The Homogeneous Maxwell Equations

240

(1)

11.2 The Lorentz Force

241

(2)

11.3 Coulomb Potential

243

(2)

12 Gravity

245

(6)

13 Closing Words

251

(4)

Part V Appendices

A Vector calculus

255

(8)

A.1 Basis Vectors

256

(1)

A.2 Change of Coordinate Systems

257

(2)

A.3 Matrix Multiplication

259

(1)

A.4 Scalars

260

(1)

A.5 Right-handed and Left-handed Coordinate Systems

260

(3)

B Calculus

263

(6)

B.1 Product Rule

263

(1)

B.2 Integration by Parts

263

(1)

B.3 The Taylor Series

264

(2)

B.4 Series

266

(1)

B.4.1 Important Series

266

(2)

B.4.2 Splitting Sums

268

(1)

B.4.3 Einstein's Sum Convention

269

(1)

B.5 Index Notation

269

(4)

B.5.1 Dummy Indices

269

(1)

B.5.2 Objects with more than One Index

270

(1)

B.5.3 Symmetric and Antisymmetric Indices

270

(1)

B.5.4 Antisymmetric x Symmetric Sums

271

(1)

B.5.5 Two Important Symbols

272

(1)

C Linear Algebra

273

(4)

C.1 Basic Transformations

273

(1)

C.2 Matrix Exponential Function

274

(1)

C.3 Determinants

274

(1)

C.4 Eigenvalues and Eigenvectors

275

(1)

C.5 Diagonalization

275

(2)

D Additional Mathematical Notions

277

(4)

D.1 Fourier Transform

277

(1)

D.2 Delta Distribution

278

(3)

Bibliography

281

(4)

Index

285

Jakob Schwichtenberg - Karlsruhe, Germany.

Physics from Symmetry Second Edition 2018 [Kietas viršelis]

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