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This textbook bridges the gap between the level of introductory courses on mechanics and electrodynamics and the level of application in high energy physics and quantum field theory. After explaining the postulates that lead to the Lorentz transformation and after going through the main points special relativity has to make in classical mechanics and electrodynamics, the authors gradually lead the reader up to a more abstract point of view on relativistic symmetry - illustrated by physical examples - until finally motivating and developing Wigner's classification of the unitary irreducible…mehr
This textbook bridges the gap between the level of introductory courses on mechanics and electrodynamics and the level of application in high energy physics and quantum field theory. After explaining the postulates that lead to the Lorentz transformation and after going through the main points special relativity has to make in classical mechanics and electrodynamics, the authors gradually lead the reader up to a more abstract point of view on relativistic symmetry - illustrated by physical examples - until finally motivating and developing Wigner's classification of the unitary irreducible representations of the inhomogeneous Lorentz group. Numerous historical and mathematical asides contribute to the conceptual clarification.
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Prof. Dr. Helmuth K. Urbantke lehrt und forscht am Institut für Theoretische Physik der Universität Wien.
Inhaltsangabe
1 The Lorentz Transformation.- 1.1 Inertial Systems.- 1.2 The Principle of Relativity.- 1.3 Consequences from the Principle of Relativity.- Appendix 1: Reciprocity of Velocities.- Appendix 2: Some Orthogonal Concomitants of Vectors.- 1.4 Invariance of the Speed of Light. Lorentz Transformation.- 1.5 The Line Element.- 1.6 Michelson, Lorentz, Poincare, Einstein.- 2 Physical Interpretation.- 2.1 Geometric Representation of Lorentz Transformations.- 2.2 Relativity of Simultaneity. Causality.- 2.3 Faster than Light.- 2.4 Lorentz Contraction.- 2.5 Retardation Effects: Invisibility of Length Contraction and Apparent Superluminal Speeds.- 2.6 Proper Time and Time Dilation.- 2.7 The Clock or Twin Paradox.- 2.8 On the Influence of Acceleration upon Clocks.- 2.9 Addition of Velocities.- 2.10 Thomas Precession.- 2.11 On Clock Synchronization.- 3 Lorentz Group, Poincare Group, and Minkowski Geometry.- 3.1 Lorentz Group and Poincare Group.- 3.2 Minkowski Space. Four-Vectors.- 3.3 Passive and ActiveTransformations. Reversals.- 3.4 Contravariant and Covariant Components. Fields.- 4 Relativistic Mechanics.- 4.1 Kinematics.- Appendix: Geometry of Relativistic Velocity Space.- 4.2 Collision Laws. Relativistic Mass Increase.- 4.3 Photons: Doppler Effect and Compton Effect.- 4.4 Conversion of Mass into Energy. Mass Defect.- 4.5 Relativistic Phase Space.- Appendix: Invariance of Rn(q).- 5 Relativistic Electrodynamics.- 5.1 Forces.- 5.2 Covariant Maxwell Equations.- 5.3 Lorentz Force.- 5.4 Tensor Algebra.- 5.5 Invariant Tensors, Metric Tensor.- 5.6 Tensor Fields and Tensor Analysis.- 5.7 The Full System of Maxwell Equations. Charge Conservation.- 5.8 Discussion of the Transformation Properties.- 5.9 Conservation Laws. Stress-Energy-Momentum Tensor.- 5.10 Charged Particles.- 6 The Lorentz Group and Some of Its Representations.- 6.1 The Lorentz Group as a Lie Group.- 6.2 The Lorentz Group as a Quasidirect Product.- 6.3 Some Subgroups of the Lorentz Group.- Appendix 1: Active Lorentz Transformations.- Appendix 2: Simplicity of the Lorentz Group L++.- 6.4 Some Representations of the Lorentz Group.- 6.5 Direct Sums and Irreducible Representations.- 6.6 Schur's Lemma.- 7 Representation Theory of the Rotation Group.- 7.1 The Rotation Group SO(3,R).- 7.2 Infinitesimal Transformations.- 7.3 Lie Algebra and Representations of SO(3).- 7.4 Lie Algebras of Lie Groups.- 7.5 Unitary Irreducible Representations of SO(3).- 7.6 SU(2), Spinors, and Representation of Finite Rotations.- 7.7 Representations on Function Spaces.- 7.8 Description of Particles with Spin.- 7.9 The Full Orthogonal Group 0(3).- 7.10 On Multivalued and Ray Representations.- 8 Representation Theory of the Lorentz Group.- 8.1 Lie Algebra and Representations of L++.- 8.2 The Spinor Representation.- 8.3 Spinor Algebra.- Appendix: Determination of the Lower Clebsch-Gordan Terms.- 8.4 The Relation between Spinors and Tensors.- Appendix 1: Spinors and Lightlike 4-Vectors.- Appendix 2: Intrinsic Classification of LorentzTransformations.- 8.5 Representations of the Full Lorentz Group.- 9 Representation Theory of the Poincaré Group.- 9.1 Fields and Field Equations. Dirac Equation.- Appendix: Dirac Spinors and Clifford-Dirac Algebra.- 9.2 Relativistic Covariance in Quantum Mechanics.- 9.3 Lie Algebra and Invariants of the Poincare Group.- 9.4 Irreducible Unitary Representations of the Poincare Group.- 9.5 Representation Theory of P++ and Local Field Equations.- 9.6 Irreducible Semiunitary Ray Representations of P.- 10 Conservation Laws in Relativistic Field Theory.- 10.1 Action Principle and Noether's Theorem.- 10.2 Application to Poincaré-Covariant Field Theory.- 10.3 Relativistic Hydrodynamics.- Appendices.- A Basic Concepts from Group Theory.- A.1 Definition of Groups.- A.2 Subgroups and Factor Groups.- A.3 Homomorphisms, Extensions, Products.- A.4 Transformation Groups.- B Abstract Multilinear Algebra.- B.1 Semilinear Maps.- B.2 Dual Space.- B.3 Complex-Conjugate Space.- B.4 Transposition, Complex,and Hermitian Conjugation.- B.5 Bi- and Sesquilinear Forms.- B.6 Real and Complex Structures.- B.7 Direct Sums.- B.8 Tensor Products.- B.9 Complexification.- B.10 The Tensor Algebra over a Vector Space.- B.11 Symmetric and Exterior Algebra.- B.12 Inner Product. Creation and Annihilation Operators.- B.13 Duality in Exterior Algebra.- C Majorana Spinors, Charge Conjugation, and Time Reversal in Dirac Theory.- C.1 Dirac Algebra Reconsidered.- C.2 Majorana Spinors, Charge Conjugation, Time Reversal.- D Poincaré Covariance in Second Quantization.- D.l The One-Particle Space.- D.2 Fock Space and Field Operator.- D.3 Poincaré Covariance and Conserved Quantities.- Notation.- Author Index.
1 The Lorentz Transformation.- 1.1 Inertial Systems.- 1.2 The Principle of Relativity.- 1.3 Consequences from the Principle of Relativity.- Appendix 1: Reciprocity of Velocities.- Appendix 2: Some Orthogonal Concomitants of Vectors.- 1.4 Invariance of the Speed of Light. Lorentz Transformation.- 1.5 The Line Element.- 1.6 Michelson, Lorentz, Poincare, Einstein.- 2 Physical Interpretation.- 2.1 Geometric Representation of Lorentz Transformations.- 2.2 Relativity of Simultaneity. Causality.- 2.3 Faster than Light.- 2.4 Lorentz Contraction.- 2.5 Retardation Effects: Invisibility of Length Contraction and Apparent Superluminal Speeds.- 2.6 Proper Time and Time Dilation.- 2.7 The Clock or Twin Paradox.- 2.8 On the Influence of Acceleration upon Clocks.- 2.9 Addition of Velocities.- 2.10 Thomas Precession.- 2.11 On Clock Synchronization.- 3 Lorentz Group, Poincare Group, and Minkowski Geometry.- 3.1 Lorentz Group and Poincare Group.- 3.2 Minkowski Space. Four-Vectors.- 3.3 Passive and ActiveTransformations. Reversals.- 3.4 Contravariant and Covariant Components. Fields.- 4 Relativistic Mechanics.- 4.1 Kinematics.- Appendix: Geometry of Relativistic Velocity Space.- 4.2 Collision Laws. Relativistic Mass Increase.- 4.3 Photons: Doppler Effect and Compton Effect.- 4.4 Conversion of Mass into Energy. Mass Defect.- 4.5 Relativistic Phase Space.- Appendix: Invariance of Rn(q).- 5 Relativistic Electrodynamics.- 5.1 Forces.- 5.2 Covariant Maxwell Equations.- 5.3 Lorentz Force.- 5.4 Tensor Algebra.- 5.5 Invariant Tensors, Metric Tensor.- 5.6 Tensor Fields and Tensor Analysis.- 5.7 The Full System of Maxwell Equations. Charge Conservation.- 5.8 Discussion of the Transformation Properties.- 5.9 Conservation Laws. Stress-Energy-Momentum Tensor.- 5.10 Charged Particles.- 6 The Lorentz Group and Some of Its Representations.- 6.1 The Lorentz Group as a Lie Group.- 6.2 The Lorentz Group as a Quasidirect Product.- 6.3 Some Subgroups of the Lorentz Group.- Appendix 1: Active Lorentz Transformations.- Appendix 2: Simplicity of the Lorentz Group L++.- 6.4 Some Representations of the Lorentz Group.- 6.5 Direct Sums and Irreducible Representations.- 6.6 Schur's Lemma.- 7 Representation Theory of the Rotation Group.- 7.1 The Rotation Group SO(3,R).- 7.2 Infinitesimal Transformations.- 7.3 Lie Algebra and Representations of SO(3).- 7.4 Lie Algebras of Lie Groups.- 7.5 Unitary Irreducible Representations of SO(3).- 7.6 SU(2), Spinors, and Representation of Finite Rotations.- 7.7 Representations on Function Spaces.- 7.8 Description of Particles with Spin.- 7.9 The Full Orthogonal Group 0(3).- 7.10 On Multivalued and Ray Representations.- 8 Representation Theory of the Lorentz Group.- 8.1 Lie Algebra and Representations of L++.- 8.2 The Spinor Representation.- 8.3 Spinor Algebra.- Appendix: Determination of the Lower Clebsch-Gordan Terms.- 8.4 The Relation between Spinors and Tensors.- Appendix 1: Spinors and Lightlike 4-Vectors.- Appendix 2: Intrinsic Classification of LorentzTransformations.- 8.5 Representations of the Full Lorentz Group.- 9 Representation Theory of the Poincaré Group.- 9.1 Fields and Field Equations. Dirac Equation.- Appendix: Dirac Spinors and Clifford-Dirac Algebra.- 9.2 Relativistic Covariance in Quantum Mechanics.- 9.3 Lie Algebra and Invariants of the Poincare Group.- 9.4 Irreducible Unitary Representations of the Poincare Group.- 9.5 Representation Theory of P++ and Local Field Equations.- 9.6 Irreducible Semiunitary Ray Representations of P.- 10 Conservation Laws in Relativistic Field Theory.- 10.1 Action Principle and Noether's Theorem.- 10.2 Application to Poincaré-Covariant Field Theory.- 10.3 Relativistic Hydrodynamics.- Appendices.- A Basic Concepts from Group Theory.- A.1 Definition of Groups.- A.2 Subgroups and Factor Groups.- A.3 Homomorphisms, Extensions, Products.- A.4 Transformation Groups.- B Abstract Multilinear Algebra.- B.1 Semilinear Maps.- B.2 Dual Space.- B.3 Complex-Conjugate Space.- B.4 Transposition, Complex,and Hermitian Conjugation.- B.5 Bi- and Sesquilinear Forms.- B.6 Real and Complex Structures.- B.7 Direct Sums.- B.8 Tensor Products.- B.9 Complexification.- B.10 The Tensor Algebra over a Vector Space.- B.11 Symmetric and Exterior Algebra.- B.12 Inner Product. Creation and Annihilation Operators.- B.13 Duality in Exterior Algebra.- C Majorana Spinors, Charge Conjugation, and Time Reversal in Dirac Theory.- C.1 Dirac Algebra Reconsidered.- C.2 Majorana Spinors, Charge Conjugation, Time Reversal.- D Poincaré Covariance in Second Quantization.- D.l The One-Particle Space.- D.2 Fock Space and Field Operator.- D.3 Poincaré Covariance and Conserved Quantities.- Notation.- Author Index.
Rezensionen
"... I wish that many readers from the large English-speaking area ... will step on it and profit from an illuminating textbook which was reserved to German-language readers up to now." Wolfgang Hasse - General Relativity and Gravitation, vol. 34, 12/2002
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