与其它传统著作不同，巴塔努尼编著的《对称和凝聚态物理学中的计算方法》首次系统地介绍了现代物理学中三个非常重要的主题：对称、凝聚态物理和计算方法以及它们之间的有机联系。本书展示了如何有效地利用群论来研究与对称性有关的实际物理问题，首先介绍了对称性，进而引入群论并详细介绍了群的表示理论、特征标的计算、直积群和空间群等，然后讲解利用群论研究固体的电子性质以及表面动力学特性，此外还包括群论在傅立叶晶体学，准晶和非公度系统中的高级应用。本书包括大量的mathematica示例程序和150多道练习，可以帮助读者进一步理解概念。本书是凝聚态物理，材料科学和化学专业的研究生的理想教材。

preface

1 symmetry and physics

 1.1 introduction

 1.2 hamiltonians, eigenfunctions, and eigenvalues

 1.3 symmetry operators and operator algebra

 1.4 point-symmetry operations

 1.5 applications to quantum mechanics

 exercises

2 symmetry and group theory

 2.1 groups and their realizations

 2.2 the symmetric group

 2.3 computational aspects

 2.4 classes

 2.5 homomorphism, isomorphism, and automorphism

 2.6 direct- or outer-product groups

 exercises

3 group representations: concepts

 3.1 representations and realizations

 3.2 generation of representations on a set of basis functions

 exercises

4 group representations: formalism and methodology

 4.1 matrix representations

 4.2 character of a matrix representation

 4.3 burnside's method

 exercises

 computational projects

5 dixon's method for computing group characters

 5.1 the eigenvalue equation modulo p

 5.2 dixon's method for irreducible characters

 5.3 computer codes for dixon's method

 appendix 1 finding eigenvalues and eigenvectors

 exercises

 appendix 2

 computation project

6 group action and symmetry projection operators

 6.1 group action

 6.2 symmetry projection operators

 6.3 the regular projection matrices: the simple characteristic

 exercises

7 construction of the irreducible representations

 7.1 eigenvectors of the regular rep

 7.2 the symmetry structure of the regular rep eigenvectors

 7.3 symmetry projection on regular rep eigenvectors

 7.4 computer construction of irreps with ds ]1

 7.5 summary of the method

 exercise

8 product groups and product representations

 8.1 introduction

 8.2 subgroups and cosets

 8.3 direct outer-product groups

 8.4 semidirect product groups

 8.5 direct inner-product groups and their representations

 8.6 product representations and the clebsch-gordan series

 8.7 computer codes

 8.8 summary

 exercises

9 induced representations

 9.1 introduction

 9.2 subduced reps and compatibility relations

 9.3 induction of group reps from the irreps of its subgroups

 9.4 irreps induced from invariant subgroups

 9.5 examples of irrep induction using the method of little-groups

 appendix frobenius reciprocity theorem and other useful theorems

 exercises

10 crystallographic symmetry and space-groups

 10.1 euclidean space

 10.2 crystallography

 10.3 the perfect crystal

 10.4 space-group operations: the seitz operators

 10.5 symmorphic and nonsymmorphic space-groups

 10.6 site-symmetries and the .wyckoff notation

 10.7 fourier space crystallography

 exercises

11 space-groups: irreps

 11.1 irreps of the translation group

 11.2 induction of irreps of space-groups

 exercises

12 time-reversal symmetry: color groups and the onsager relations

 12.1 introduction

 12.2 the time-reversal operator in quantum mechanics

 12.3 spin-l/2 and double-groups

 12.4 magnetic and color groups

 12.5 the time-reversed representation: theory of corepresentations

 12.6 theory of crystal fields

 12.7 onsager reciprocity theorem (onsager relations) and transport properties

 exercises

13 tensors and tensor fields

 13.1 tensors and their space-time symmetries

 13.2 construction of symmetry-adapted tensors

 13.3 description and classification of matter tensors

 13.4 tensor field representations

 exercises

14 electronic properties of solids

 14.1 introduction

 14.2 the one-electron approximations and self-consistent-field theories

 14.3 methods and techniques for band structure calculations

 14.4 electronic structure of magnetically ordered systems

 appendix i derivation of the hartree-fock equations

 appendix 2 holstein-primakoff (hp) operators

 exercises

15 dynamical properties of molecules, solids, and surfaces

 15.1 introduction

 15.2 dynamical properties of molecules

 15.3 dynamical properties of solids

 15.4 dynamical properties of surfaces

 appendix 1 coulomb interactions and the method of ewald summation

 appendix 2 electronic effects on phonons in insulators and semiconductors

 exercises

16 experimental measurements and selection rules

 16.1 introduction

 16.2 selection rules

 16.3 differential scattering cross-sections in the born approximation

 16.4 light scattering spectroscopies

 16.5 photoemission and dipole selection rules

 16.6 neutron and atom scattering spectroscopies

 exercises

 17.1 phase transitions and their classification

 17.2 landau theory of phase transitions: principles

 17.3 construction and minimization techniques for △φ

 exercises

18 incommensurate systems and quasi-crystals

 18.1 introduction

 18.2 the concept of higher-dimensional spaces: superspaces and superlattices

 18.3 quasi-crystal symmetry: the notion of indistinguishability and the clossification of space-groups

 18.4 two-dimensional lattices, cyclotomic integers, and axial stacking

bibliography

references

index