This textbook attempts to bridge the gap that exists between the two levels on which relativistic symmetry is usually presented - the level of introductory courses on mechanics and electrodynamics and the level of application in high energy physics and quantum field theory: in both cases, too many other topics are more important and hardly leave time for a deepening of the idea of relativistic symmetry. So 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 - always illustrating it 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 conceptual clarification.
Author(s): Roman U. Sexl, Helmuth K. Urbantke, H.K. Urbantke
Edition: 1
Publisher: Springer
Year: 2000
Language: English
Pages: 400
Contents......Page all_18324_to_00400.cpc0008.djvu
1.1 Inertial Systems......Page all_18324_to_00400.cpc0012.djvu
1.2 The Principle of Relativity......Page all_18324_to_00400.cpc0014.djvu
1.3 Consequences from the Principle of Relativity......Page all_18324_to_00400.cpc0015.djvu
Appendix 2: Some Orthogonal Concomitants of Vectors......Page all_18324_to_00400.cpc0018.djvu
1.4 Invariance of the Speed of Light. Lorentz Transformation......Page all_18324_to_00400.cpc0019.djvu
1.5 The Line Element......Page all_18324_to_00400.cpc0021.djvu
1.6 Michelson, Lorentz, Poincaré, Einstein......Page all_18324_to_00400.cpc0024.djvu
2.1 Geometric Representation of Lorentz Transformations......Page all_18324_to_00400.cpc0030.djvu
2.2 Relativity of Simultaneity. Causality......Page all_18324_to_00400.cpc0032.djvu
2.3 Faster than Light......Page all_18324_to_00400.cpc0035.djvu
2.4 Lorentz Contraction......Page all_18324_to_00400.cpc0039.djvu
2.5 Retardation Effects: Invisibility of Length Contraction and Apparent Superluminal Speeds......Page all_18324_to_00400.cpc0040.djvu
2.6 Proper Time and Time Dilation......Page all_18324_to_00400.cpc0043.djvu
2.7 The Clock or Twin Paradox......Page all_18324_to_00400.cpc0045.djvu
2.8 On the Influence of Acceleration upon Clocks......Page all_18324_to_00400.cpc0048.djvu
2.9 Addition of Velocities......Page all_18324_to_00400.cpc0049.djvu
2.10 Thomas Precession......Page all_18324_to_00400.cpc0051.djvu
2.11 On Clock Synchronization......Page all_18324_to_00400.cpc0054.djvu
3 Lorentz Group, Poincaré Group, and Minkowski Geometry......Page all_18324_to_00400.cpc0060.djvu
3.1 Lorentz Group and Poincaré Group......Page all_18324_to_00400.cpc0061.djvu
3.2 Minkowski Space. Four-Vectors......Page all_18324_to_00400.cpc0063.djvu
3.3 Passive and Active Transformations. Reversals......Page all_18324_to_00400.cpc0068.djvu
3.4 Contravariant and Covariant Components. Fields......Page all_18324_to_00400.cpc0070.djvu
4.1 Kinematics......Page all_18324_to_00400.cpc0074.djvu
Appendix: Geometry of Relativistic Velocity Space......Page all_18324_to_00400.cpc0077.djvu
4.2 Collision Laws. Relativistic Mass Increase......Page all_18324_to_00400.cpc0078.djvu
4.3 Photons: Doppler Effect and Compton Effect......Page all_18324_to_00400.cpc0081.djvu
4.4 Conversion of Mass into Energy. Mass Defect......Page all_18324_to_00400.cpc0086.djvu
4.5 Relativistic Phase Space......Page all_18324_to_00400.cpc0089.djvu
Appendix: Invariance of R_n(q)......Page all_18324_to_00400.cpc0094.djvu
5.1 Forces......Page all_18324_to_00400.cpc0096.djvu
5.2 Covariant Maxwell Equations......Page all_18324_to_00400.cpc0097.djvu
5.3 Lorentz Force......Page all_18324_to_00400.cpc0102.djvu
5.4 Tensor Algebra......Page all_18324_to_00400.cpc0103.djvu
5.5 Invariant Tensors, Metric Tensor......Page all_18324_to_00400.cpc0106.djvu
5.6 Tensor Fields and Tensor Analysis......Page all_18324_to_00400.cpc0113.djvu
5.7 The Full System of Maxwell Equations. Charge Conservation......Page all_18324_to_00400.cpc0116.djvu
5.8 Discussion of the Transformation Properties......Page all_18324_to_00400.cpc0119.djvu
5.9 Conservation Laws. Stress-Energy-Momentum Tensor......Page all_18324_to_00400.cpc0126.djvu
5.10 Charged Particles......Page all_18324_to_00400.cpc0133.djvu
6.1 The Lorentz Group as a Lie Group......Page all_18324_to_00400.cpc0145.djvu
6.2 The Lorentz Group as a Quasidirect Product......Page all_18324_to_00400.cpc0150.djvu
6.3 Some Subgroups of the Lorentz Group......Page all_18324_to_00400.cpc0154.djvu
Appendix 1: Active Lorentz Transformations......Page all_18324_to_00400.cpc0156.djvu
Appendix 2: Simplicity of the Lorentz Group L^\uparrow_+......Page all_18324_to_00400.cpc0157.djvu
6.4 Some Representations of the Lorentz Group......Page all_18324_to_00400.cpc0159.djvu
6.5 Direct Sums and Irreducible Representations......Page all_18324_to_00400.cpc0164.djvu
6.6 Schur's Lemma......Page all_18324_to_00400.cpc0170.djvu
7 Representation Theory of the Rotation Group......Page all_18324_to_00400.cpc0180.djvu
7.1 The Rotation Group SO(3,R)......Page all_18324_to_00400.cpc0181.djvu
7.2 Infinitesimal Transformations......Page all_18324_to_00400.cpc0184.djvu
7.3 Lie Algebra and Representations of SO(3)......Page all_18324_to_00400.cpc0187.djvu
7.4 Lie Algebras of Lie Groups......Page all_18324_to_00400.cpc0190.djvu
7.5 Unitary Irreducible Representations of SO(3)......Page all_18324_to_00400.cpc0194.djvu
7.6 SU(2), Spinors, and Representation of Finite Rotations......Page all_18324_to_00400.cpc0206.djvu
7.7 Representations on Function Spaces......Page all_18324_to_00400.cpc0217.djvu
7.8 Description of Particles with Spin......Page all_18324_to_00400.cpc0223.djvu
7.9 The Full Orthogonal Group O(3)......Page all_18324_to_00400.cpc0229.djvu
7.10 On Multivalued and Ray Representations......Page all_18324_to_00400.cpc0235.djvu
8.1 Lie Algebra and Representations of L^\uparrow_+......Page all_18324_to_00400.cpc0240.djvu
8.2 The Spinor Representation......Page all_18324_to_00400.cpc0247.djvu
8.3 Spinor Algebra......Page all_18324_to_00400.cpc0253.djvu
Appendix: Determination of the Lower Clebsch-Gordan Terms......Page all_18324_to_00400.cpc0257.djvu
8.4 The Relation between Spinors and Tensors......Page all_18324_to_00400.cpc0258.djvu
Appendix 1: Spinors and Lightlike 4-Vectors......Page all_18324_to_00400.cpc0263.djvu
Appendix 2: Intrinsic Classification of Lorentz Transformations......Page all_18324_to_00400.cpc0264.djvu
8.5 Representations of the Full Lorentz Group......Page all_18324_to_00400.cpc0266.djvu
9.1 Fields and Field Equations. Dirac Equation......Page all_18324_to_00400.cpc0272.djvu
Appendix: Dirac Spinors and Clifford-Dirac Algebra......Page all_18324_to_00400.cpc0276.djvu
9.2 Relativistic Covariance in Quantum Mechanics......Page all_18324_to_00400.cpc0282.djvu
9.3 Lie Algebra and Invariants of the Poincaré Group......Page all_18324_to_00400.cpc0289.djvu
9.4 Irreducible Unitary Representations of the Poincaré Group......Page all_18324_to_00400.cpc0296.djvu
9.5 Representation Theory of P^\uparrow_+ and Local Field Equations......Page all_18324_to_00400.cpc0310.djvu
9.6 Irreducible Semiunitary Ray Representations of P......Page all_18324_to_00400.cpc0324.djvu
10 Conservation Laws in Relativistic Field Theory......Page all_18324_to_00400.cpc0328.djvu
10.1 Action Principle and Noether's Theorem......Page all_18324_to_00400.cpc0329.djvu
10.2 Application to Poincaré-Covariant Field Theory......Page all_18324_to_00400.cpc0334.djvu
10.3 Relativistic Hydrodynamics......Page all_18324_to_00400.cpc0342.djvu
A.2 Subgroups and Factor Groups......Page all_18324_to_00400.cpc0347.djvu
A.3 Homomorphisms, Extensions, Products......Page all_18324_to_00400.cpc0348.djvu
A.4 Transformation Groups......Page all_18324_to_00400.cpc0350.djvu
B.1 Semilinear Maps......Page all_18324_to_00400.cpc0351.djvu
B.3 Complex-Conjugate Space......Page all_18324_to_00400.cpc0352.djvu
B.5 Bi- and Sesquilinear Forms......Page all_18324_to_00400.cpc0353.djvu
B.6 Real and Complex Structures......Page all_18324_to_00400.cpc0354.djvu
B.8 Tensor Products......Page all_18324_to_00400.cpc0355.djvu
B.9 Complexification......Page all_18324_to_00400.cpc0356.djvu
B.10 The Tensor Algebra over a Vector Space......Page all_18324_to_00400.cpc0357.djvu
B.11 Symmetric and Exterior Algebra......Page all_18324_to_00400.cpc0358.djvu
B.12 Inner Product. Creation and Annihilation Operators......Page all_18324_to_00400.cpc0360.djvu
B.13 Duality in Exterior Algebra......Page all_18324_to_00400.cpc0361.djvu
B. 14 G-Geometries and Quantities of Type (G,\sigma)......Page all_18324_to_00400.cpc0364.djvu
C.1 Dirac Algebra Reconsidered......Page all_18324_to_00400.cpc0368.djvu
C.2 Majorana Spinors, Charge Conjugation, Time Reversal......Page all_18324_to_00400.cpc0370.djvu
D.1 The One-Particle Space......Page all_18324_to_00400.cpc0373.djvu
D.2 Fock Space and Field Operator......Page all_18324_to_00400.cpc0375.djvu
D.3 Poincaré Covariance and Conserved Quantities......Page all_18324_to_00400.cpc0377.djvu
Notation......Page all_18324_to_00400.cpc0380.djvu
Bibliography......Page all_18324_to_00400.cpc0384.djvu
Author Index......Page all_18324_to_00400.cpc0390.djvu
Subject Index......Page all_18324_to_00400.cpc0393.djvu
