## Group Theory in Physics, Volume 1An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems.Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry.Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained.A set of problems and solutions has been published in a separate booklet. |

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### Contents

INTRODUCTION I | 1 |

BASIC GROUP THEORY | 12 |

GROUP REPRESENTATIONS | 27 |

GENERAL PROPERTIES OF IRREDUCIBLE | 54 |

REPRESENTATIONS OF THE SYMMETRIC | 64 |

ONEDIMENSIONAL CONTINUOUS GROUPS | 80 |

ROTATIONS IN THREEDIMENSIONAL | 94 |

THE GROUP SU2 AND MORE ABOUT SO3 | 125 |

SPACE INVERSION INVARIANCE | 212 |

Parity | 238 |

TIME REVERSAL INVARIANCE | 245 |

FINITEDIMENSIONAL REPRESENTATIONS | 262 |

NOTATIONS AND SYMBOLS | 292 |

GROUP ALGEBRA AND THE REDUCTION | 307 |

SUPPLEMENTS TO THE THEORY | 314 |

ROTATIONAL AND LORENTZ SPINORS | 320 |

EUCLIDEAN GROUPS IN TWO | 152 |

THE LORENTZ AND POINCARE GROUPS | 173 |

Transformations | 179 |

UNITARY REPRESENTATIONS OF | 328 |

335 | |

### Other editions - View all

Group Theory in Physics: An Introduction to Symmetry Principles, Group ... Wu-Ki Tung Limited preview - 1985 |

### Common terms and phrases

3-dimensional angular momentum anti-symmetric Appendix apply arbitrary basis vectors Chap chapter Clebsch-Gordan coefficients commutes components conjugate contravariant coordinate corresponding cosets covariant defined Definition denoted derive direct product discussed eigenstates eigenvalue eigenvectors equation equivalent Euclidean group Example factor group finite dimensional given by Eq GL(m group algebra group elements group G group multiplication group representation group SO(3 group theory helicity hence hermitian idempotent identity indices integer invariant subgroup invariant subspace invariant tensor irreducible representations isomorphic Lemma Lie algebra linear transformations little group Lorentz boosts Lorentz group Lorentz transformations mathematical matrix elements notation obtain orthogonal parameter parity particle permutation physical system Poincare group projection operators Proof properties quantum mechanical relations representation matrices representation space respect reversal right-hand side satisfy space inversion spin spinors symmetry group tableau tations tensor space Theorem translations unitary irreducible representations vector space wave function Young diagram Young tableau