## 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 |

The 14 Bravais lattices | 311 |

Further reading | 424 |

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### Common terms and phrases

action of G atom axis basis character table coefficients compact support component compute conjugacy class consider consists corresponding crystal decomposes decomposition define density determined diagonal differential dimensional direct sum eigenvalue eigenvector electron elements energy entries equation equivalent example finite finite-dimensional fixed point follows formula frequencies G acts G x G given gives group G hence Hilbert space identity induced representations integer invariant subspace irreducible representations isomorphic isotropy group lattice lemma Lie algebra linear combinations linear transformation lines matrix molecule multiplication obtain occurs one-dimensional operator orbit orthogonal particles permutation plane Poincare group proof prove quantum mechanics quarks radiation representation of G rotation satisfying scalar product Schur's lemma Sl(d smooth spanned spectra spectrum spin subgroup subset Suppose symmetry group tabloid tensor product theorem theory topological transition values vector bundle vector space vertices vibrations weight vector write Young diagram zero