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**Relativity, groups, particles. Special relativity and relativistic symmetry in field and particle physics. Revised and transl. from the 3rd German edition by H. K. Urbantke.**
*(English)*
Zbl 1057.83001

Wien: Springer (ISBN 3-211-83443-5). xii, 388 p. (2001).

Publisher’s description: 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.

Contents: 1. The Lorentz transformation; 2. Physical interpretation; 3. Lorentz group, Poincaré group and Minkowski geometry; 4. Relativistic mechanics; 5. Relativistic electrodynamics; 6. The Lorentz group and some of its representations; 7. Representation theory of the rotation group; 8. Representation theory of the Lorentz group; 9. Representation theory of the Poincaré group; 10. Conservation laws in relativistic field theories.

The four appendices serve as background for the understanding of the main text: A. Basic concepts of group theory; B. Abstract multilinear algebra; C. Majorana spinors, charge conjugation and time reversal in Dirac theory; D. Poincaré covariance in second quantization.

For earlier editions see Zbl 0966.83501 and Zbl 0966.83502.

Contents: 1. The Lorentz transformation; 2. Physical interpretation; 3. Lorentz group, Poincaré group and Minkowski geometry; 4. Relativistic mechanics; 5. Relativistic electrodynamics; 6. The Lorentz group and some of its representations; 7. Representation theory of the rotation group; 8. Representation theory of the Lorentz group; 9. Representation theory of the Poincaré group; 10. Conservation laws in relativistic field theories.

The four appendices serve as background for the understanding of the main text: A. Basic concepts of group theory; B. Abstract multilinear algebra; C. Majorana spinors, charge conjugation and time reversal in Dirac theory; D. Poincaré covariance in second quantization.

For earlier editions see Zbl 0966.83501 and Zbl 0966.83502.

### MSC:

83-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory |

81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |

22E70 | Applications of Lie groups to the sciences; explicit representations |

81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |

81R40 | Symmetry breaking in quantum theory |

83-03 | History of relativity and gravitational theory |

83A05 | Special relativity |