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Geometry, Symmetries, and Classical Physics: A Mosaic [Hardback]

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  • Formāts: Hardback, 482 pages, height x width: 254x178 mm, weight: 1002 g, 6 Tables, black and white; 43 Line drawings, black and white; 43 Illustrations, black and white
  • Izdošanas datums: 29-Dec-2021
  • Izdevniecība: CRC Press
  • ISBN-10: 0367535238
  • ISBN-13: 9780367535230
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Geometry, Symmetries, and Classical Physics: A MosaicPalielināt
  • Formāts: Hardback, 482 pages, height x width: 254x178 mm, weight: 1002 g, 6 Tables, black and white; 43 Line drawings, black and white; 43 Illustrations, black and white
  • Izdošanas datums: 29-Dec-2021
  • Izdevniecība: CRC Press
  • ISBN-10: 0367535238
  • ISBN-13: 9780367535230
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780367535230.html
Keywords:
This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics.

Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume.

Key features:











Contains a modern, streamlined presentation of classical topics, which are normally taught separately





Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity





Focuses on the clear presentation of the mathematical notions and calculational technique

Recenzijas

'Geometry, Symmetries, and Classical Physics - A Mosaic" by Manousos Markoutsakis is a remarkable journey through the intertwined worlds of geometry and classical physics with a particular focus on symmetries. The author has crafted a book that not only educates but also inspires readers to delve deeper into the profound connections between these fields. One of the strengths of this book is its approachability. The author has described the mathematics behind the subject quite nicely with a great clarity. The book is also made accessible to a wide range of readers, from physics enthusiasts to students and researchers. The book's organization is also a highlight. It leads the reader through a logical progression, building on previously discussed concepts and culminating in a comprehensive understanding of the role of symmetries in classical physics. While the book excels in many aspects, it is worth noting that some sections may challenge readers without a strong mathematical background. However, this should not deter anyone from exploring the book, as the author's explanations and insights are valuable even for those who may not grasp every mathematical detail. Most importantly, the physics behind a mathematical expression is well-described. I think it is a good addition to the literature on physics and geometry. It serves as an enlightening mosaic that beautifully illustrates the profound connections between these fields.'

- Prof. Dr. Taushif Ahmed, Universität Regensburg, September, 2023. 'Geometry, Symmetries, and Classical Physics - A Mosaic" by Manousos Markoutsakis is a remarkable journey through the intertwined worlds of geometry and classical physics with a particular focus on symmetries. The author has crafted a book that not only educates but also inspires readers to delve deeper into the profound connections between these fields. One of the strengths of this book is its approachability. The author has described the mathematics behind the subject quite nicely with a great clarity. The book is also made accessible to a wide range of readers, from physics enthusiasts to students and researchers. The book's organization is also a highlight. It leads the reader through a logical progression, building on previously discussed concepts and culminating in a comprehensive understanding of the role of symmetries in classical physics. While the book excels in many aspects, it is worth noting that some sections may challenge readers without a strong mathematical background. However, this should not deter anyone from exploring the book, as the author's explanations and insights are valuable even for those who may not grasp every mathematical detail. Most importantly, the physics behind a mathematical expression is well-described. I think it is a good addition to the literature on physics and geometry. It serves as an enlightening mosaic that beautifully illustrates the profound connections between these fields.'

- Prof. Dr. Taushif Ahmed, Universität Regensburg, September, 2023.

Preface xi
Part I Geometric Manifolds
1 Manifolds and Tensors
3(20)
1.1 Differentiation in Several Dimensions
3(4)
1.2 Differentiable Manifolds
7(4)
1.3 Tangent Structure, Vectors and Covectors
11(5)
1.4 Vector Fields and the Commutator
16(4)
1.5 Tensor Fields on Manifolds
20(3)
2 Geometry and Integration on Manifolds
23(30)
2.1 Geometry and Metric
23(8)
2.2 Isometry and Conformality
31(1)
2.3 Examples of Geometries
32(7)
2.4 Differential Forms and the Exterior Derivative
39(4)
2.5 Integrals of Differential Forms
43(4)
2.6 Theorem of Stokes
47(6)
3 Symmetries of Manifolds
53(14)
3.1 Transformations and the Lie Derivative
53(5)
3.2 Symmetry Transformations of Manifolds
58(2)
3.3 Isometric and Conformal Killing Vectors
60(1)
3.4 Euclidean and Scale Transformations
61(6)
Part II Mechanics and Symmetry
4 Newtonian Mechanics
67(18)
4.1 Galileian Spacetime
67(3)
4.2 Newton's Laws of Mechanics
70(4)
4.3 Systems of Particles and Conserved Quantities
74(4)
4.4 Gravitation and the Shell Theorem
78(7)
5 Lagrangian Methods and Symmetry
85(14)
5.1 Applying the Principle of Stationary Action
85(6)
5.2 Noether's Theorem in Mechanics
91(3)
5.3 Galilei Symmetry and Conservation
94(5)
6 Relativistic Mechanics
99(24)
6.1 Lorentz Transformations
99(3)
6.2 Minkowski Spacetime
102(10)
6.3 Relativistic Particle Mechanics
112(4)
6.4 Lagrangian Formulation
116(2)
6.5 Relativistic Symmetry and Conservation
118(5)
Part III Symmetry Groups and Algebras
7 Lie Groups
123(12)
7.1 Notion of a Group
123(3)
7.2 Notion of a Group Representation
126(2)
7.3 Lie Groups and Matrix Groups
128(7)
8 Lie Algebras
135(12)
8.1 Matrix Exponential and the BCH Formula
135(4)
8.2 Lie Algebra of a Lie Group
139(2)
8.3 Abstract Lie Algebras and Matrix Algebras
141(6)
9 Representations
147(12)
9.1 Representations of Groups and Algebras
147(2)
9.2 Adjoint Representations
149(2)
9.3 Tensor and Function Representations
151(1)
9.4 Symmetry Transformations of Tensor Fields
152(3)
9.5 Induced Representations
155(1)
9.6 Lie Algebra of Killing Vector Fields
155(4)
10 Rotations and Euclidean Symmetry
159(10)
10.1 Rotation Group
159(3)
10.2 Rotation Algebra
162(2)
10.3 Translations and the Euclidean Group
164(2)
10.4 Euclidean Algebra
166(3)
11 Boosts and Galilei Symmetry
169(6)
11.1 Group of Boosts
169(3)
11.2 Group of Boosts and Rotations
172(1)
11.3 Galilei Group
173(1)
11.4 Galilei Algebra
173(2)
12 Lorentz Symmetry
175(22)
12.1 Lorentz Group
175(2)
12.2 Spinor Representation of the Lorentz Group
177(6)
12.3 Lorentz Algebra
183(4)
12.4 Representation on Scalars, Vectors and Tensors
187(1)
12.5 Representation on Weyl and Dirac Spinors
188(6)
12.6 Representation on Fields
194(3)
13 Poincare Symmetry
197(8)
13.1 Meaning of Poincare Transformations
197(1)
13.2 Poincare Group
197(3)
13.3 Poincare Algebra and Field Representations
200(2)
13.4 Correspondence of Spacetime Symmetries
202(3)
14 Conformal Symmetry
205(20)
14.1 Conformal Group
205(7)
14.2 Conformal Algebra
212(4)
14.3 Field Transformations
216(2)
14.4 Linearization of the Conformal Group
218(7)
Part IV Classical Fields
15 Lagrangians and Noether's Theorem
225(22)
15.1 Introducing Fields
225(3)
15.2 Action Principle for Fields
228(3)
15.3 Scalar Fields
231(2)
15.4 Spinor Fields
233(2)
15.5 Maxwell Vector Field
235(7)
15.6 Noether's Theorem in Field Theory
242(5)
16 Spacetime Symmetries of Fields
247(20)
16.1 Spacetime Symmetries and Currents
247(4)
16.2 Versions of the Energy-Momentum Tensor
251(8)
16.3 Conserved Integrals
259(3)
16.4 Conditions for Conformal Symmetry
262(5)
17 Gauge Symmetry
267(12)
17.1 Internal Symmetries and Charge Conservation
267(1)
17.2 Interactions and the Gauge Principle
268(3)
17.3 Scalar Electrodynamics
271(1)
17.4 Spinor Electrodynamics
272(7)
Part V Riemannian Geometry
18 Connection and Geodesies
279(20)
18.1 Connection and the Covariant Derivative
279(3)
18.2 Formulae for the Covariant Derivative
282(5)
18.3 The Levi-Civita Connection
287(5)
18.4 Parallel Transport and Geodesic Curves
292(7)
19 Riemannian Curvature
299(16)
19.1 Manifestation of Curvature
299(2)
19.2 The Riemann Curvature Tensor
301(4)
19.3 Algebraic Symmetries
305(1)
19.4 Bianchi Identity and the Einstein Tensor
306(2)
19.5 Ricci Decomposition and the Weyl Tensor
308(7)
20 Symmetries of Riemannian Manifolds
315(16)
20.1 Symmetric Spaces
315(4)
20.2 Weyl Rescalings
319(2)
20.3 The Weyl-Schouten Theorem
321(4)
20.4 Group of Diffeomorphisms
325(6)
Part VI General Relativity and Symmetry
21 Einstein's Gravitation
331(24)
21.1 Physics in Curved Spacetimes
331(6)
21.2 The Einstein Equations
337(5)
21.3 Schwarzschild Metric
342(4)
21.4 Asymptotically Flat Spacetimes
346(9)
22 Lagrangian Formulation
355(22)
22.1 Action Principle in Curved Spacetimes
355(3)
22.2 The Action for Matter Fields
358(4)
22.3 The Action for the Gravitational Field
362(6)
22.4 Diffeomorphisms and Noether Currents
368(9)
23 Conservation Laws and Further Symmetries
377(22)
23.1 Locally and Globally Conserved Quantities
377(4)
23.2 On the Energy of Spacetime
381(2)
23.3 Komar Integrals
383(4)
23.4 Weyl Rescaling Symmetry
387(12)
Part VII Appendices
A Notation and Conventions
399(6)
A.1 Physical Units and Dimensions
399(2)
A.2 Mathematical Conventions
401(2)
A.3 Abbreviations
403(2)
B Mathematical Tools
405(40)
B.1 Tensor Algebra
405(13)
B.2 Matrix Exponential
418(1)
B.3 Pauli and Dirac Matrices
419(3)
B.4 Dirac Delta Distribution
422(3)
B.5 Poisson and Wave Equation
425(5)
B.6 Variational Calculus
430(4)
B.7 Volume Element and Hyperspheres
434(6)
B.8 Hypersurface Elements
440(5)
C Weyl Rescaling Formulae
445(6)
D Spaces and Symmetry Groups
451(2)
Bibliography 453(4)
Index 457
Manousos Markoutsakis is the Director of AI and HPC (Europe) at DataDirect Networks Inc, where he is responsible for managing the company's engagements in industry and academic institutions. Previously, he worked at IBM, where he was responsible for the company's private-public collaborations in European research and industry. He graduated in physics at the University of Heidelberg, where he worked on nonperturbative QCD. Manousos is a member of the German Physical Society (DPG) and the Bitkom Association.