## Group Theory and PhysicsThis book is an introduction to group theory and its application to physics. The author considers the physical applications and develops mathematical theory in a presentation that is unusually cohesive and well-motivated. The book discusses many modern topics including molecular vibrations, homogeneous vector bundles, compact groups and Lie groups, and there is much discussion of the group SU(n) and its representations, which is of great significance in elementary particle physics. The author also considers applications to solid-state physics. This is an essential resource for senior undergraduates and researchers in physics and applied mathematics. |

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### Contents

Basic definitions and examples | 1 |

Representation theory of finite groups | 48 |

Molecular vibrations and homogeneous vector bundles | 94 |

Compact groups and Lie groups | 172 |

The irreducible representations of SUn | 246 |

classes | 309 |

symmetric group | 327 |

S Dimension formulas | 348 |

groups | 407 |

Further reading | 424 |

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### Common terms and phrases

action acts algebra apply associated assume atom basis called Chapter character choose clearly combination compact completely component compute consider consists constant contains continuous corresponding decomposition define definition denote describe determined diagram dimensional direct eigenvalue electron elements energy entries equation equivalent example existence expression fact finite fixed follows formula function given gives group G hence identity induced integer interaction invariant irreducible representations lattice linear lines mass matrix means molecule multiplication Notice observed obtain occurs operator orbit orthogonal particles particular permutation physics plane positive possible proof prove quantum quantum mechanics reflection representation of G representative result rotation rule satisfying scalar side smooth spanned spectrum subgroup subspace Suppose symmetry Table tensor theorem theory transformation transition values various vector space weight write