Relativity, Groups, Particles

Produktbeschreibung

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. 

Inhaltsverzeichnis

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. 

Kritik

"... 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 

Autoreninfo

Prof. Dr. Helmuth K. Urbantke lehrt und forscht am Institut für Theoretische Physik der Universität Wien.