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　　本书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 simplecharacteristic

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 oflittle-groups

appendix frobenius reciprocity theorem and other usefultheorems

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 onsagerrelations

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 ofcorepresentations

12.6 theory of crystal fields

12.7 onsager reciprocity theorem (onsager relations) and transportproperties

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-fieldtheories

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 ewaldsummation

appendix 2 electronic effects on phonons in insulators andsemiconductors

exercises

16 experimental measurements and selection rules

16.1 introduction

16.2 selection rules

16.3 differential scattering cross-sections in the bornapproximation

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 andsuperlattices

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

18.4 two-dimensional lattices, cyclotomic integers, and axialstacking

bibliography

references

index

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书籍介绍

《对称和凝聚态物理学中的计算方法》内容简介：The main emphasis， throughout this book， is on exposing the conceptual building blocksof this mathematical theory of symmetry． Consequently， we frequently skip over long detailed mathematical proofs which can be found in a multitude of textbooks． Instead， we point the reader to references where such proofs are clearly presented． Moreover， in contrast to previous texts on the subject， the different aspects of group theory are presented wherever they are needed rather than being lumped into one single expose． This has the merit of associating a certain aspect of the theory with a tangible physical attribute． Thus， for example， we defer the introduction of cosets and invariant subgroups till we discuss spacegroups， where they find immediate application．