## Symmetry and Condensed Matter Physics: A Computational ApproachUnlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; as well as concepts and techniques behind the Landau theory of phase transitions. Adopting a computational approach to the application of group theoretical techniques to solving symmetry related problems, it dramatically alleviates the need for intensive calculations usually found in the presentation of symmetry. Writing computer programs helps the student achieve a firm understanding of the underlying concepts, and sample programs, based on Mathematica, are presented throughout the book. Containing over 150 exercises, this textbook is ideal for graduate students in condensed matter physics, materials science, and chemistry. Solutions and computer programs are available online at www.cambridge.org/9780521828451. |

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### Contents

1 | |

21 | |

concepts | 51 |

formalism and methodology | 69 |

Dixons method for computing group characters | 96 |

Group action and symmetry projection operators | 134 |

Construction of the irreducible representations | 164 |

Product groups and product representations | 179 |

Irreps | 362 |

color groups and the Onsager relations | 409 |

Tensors and tensor ﬁelds | 474 |

Electronic properties of solids | 552 |

Dynamical properties of molecules solids and surfaces | 638 |

Experimental measurements and selection rules | 716 |

Landaus theory of phase transitions | 777 |

Incommensurate systems and quasicrystals | 858 |

Induced representations | 217 |

Crystallographic symmetry and spacegroups | 263 |

### Common terms and phrases

atomic augmented matrix axis basis functions belong Bravais classes Bravais lattice Brillouin zone character coeﬃcients components computational conﬁguration conjugate Irreps consider construct coordinate corresponding coset coset representatives crystal crystallographic cubic deﬁned deﬁnition denote density determine dichromatic diﬀerent diﬀraction dimension eﬀect eigenvalue eigenvectors electron energy equation equivalent Example ﬁeld ﬁnd ﬁnite ﬁrst given group C3v group elements group theory Hamiltonian holohedry identity integer invariant inverse irreducible Irreps isomorphic Kronecker product lattice vector linear little-group magnetic matrix representatives multiplication table nonsymmorphic normal subgroup obtain orbit orthogonal permutation phase transition phonon physical plane point-group point-group operations polar polynomials potential primitive cell projection operator reﬂection relations representation respect rotation scattering space space-group spin structure subduction symmetry group symmetry operations tensor time-reversal transformation translation two-dimensional unit cell unitary wavefunction wavevector write Wyckoﬀ