Problems & solutions in group theory for physicists / Zhong-Qi Ma, Xiao-Yan Gu.

Format:

Book

Author/Creator:

Ma, Zhongqi, 1940-

Contributor:

Gu, X. Y. (Xiao-Yan)

Craig M. Merrihue Memorial Fund.

Language:

English

Subjects (All):

Group theory.

Mathematical physics.

Physical Description:

x, 464 pages : illustrations ; 24 cm

Other Title:

Problems and solutions in group theory for physicists

Group theory for physicists

Place of Publication:

River Edge, N.J. : World Scientific, [2004]

Summary:

Ma and Gu, both affiliated with the Institute of High Energy Physics in China, explain fundamentals of group theory. A beginning chapter reviews linear algebra, and subsequent chapters cover the concepts of a group and its subsets, the theory of representations of a group, and three-dimensional rotation groups. The remainder of the book is devoted to properties of some important symmetry groups of physical systems. Numerous exercises and solutions are included. The book is aimed at graduate students in physics who are studying group theory and its application to physics. It is also suitable for graduate students in theoretical chemistry. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Contents:

1. Review on Linear Algebras 1

1.1 Eigenvalues and Eigenvectors of a Matrix 1

1.2 Some Special Matrices 4

1.3 Similarity Transformation 7

2. Group and Its Subsets 27

2.1 Definition of a Group 27

2.2 Subsets in a Group 29

2.3 Homomorphism of Groups 33

3. Theory of Representations 43

3.1 Transformation Operators for a Scalar Function 43

3.2 Inequivalent and Irreducible Representations 47

3.3 Subduced and Induced Representations 65

3.4 The Clebsch-Gordan Coefficients 79

4. Three-Dimensional Rotation Group 115

4.1 SO(3) Group and Its Covering Group SU(2) 115

4.2 Inequivalent and Irreducible Representations 123

4.3 Lie Groups and Lie Theorems 140

4.4 Irreducible Tensor Operators 146

4.5 Unitary Representations with Infinite Dimensions 166

5. Symmetry of Crystals 173

5.1 Symmetric Operations and Space Groups 173

5.2 Symmetric Elements 177

5.3 International Notations for Space Groups 186

6. Permutation Groups 193

6.1 Multiplication of Permutations 193

6.2 Young Patterns, Young Tableaux and Young Operators 197

6.3 Primitive Idempotents in the Group Algebra 205

6.4 Irreducible Representations and Characters 211

6.5 The Inner and Outer Products of Representations 237

7. Lie Groups and Lie Algebras 269

7.1 Classification of Semisimple Lie Algebras 269

7.2 Irreducible Representations and the Chevalley Bases 279

7.3 Reduction of the Direct Product of Representations 299

8. Unitary Groups 317

8.1 The SU(N) Group and Its Lie Algebra 317

8.2 Irreducible Tensor Representations of SU(N) 321

8.3 Orthonormal Bases for Irreducible Representations 336

8.4 Subduced Representations 362

8.5 Casimir Invariants of SU(N) 369

9. Real Orthogonal Groups 375

9.1 Tensor Representations of SO(N) 375

9.2 Spinor Representations of SO(N) 403

9.3 SO(4) Group and the Lorentz Group 415

10. The Symplectic Groups 433

10.1 The Groups Sp(2l, R) and USp(2l) 433

10.2 Irreducible Representations of Sp(2l) 440.

Notes:

Includes bibliographical references (pages 457-459) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Craig M. Merrihue Memorial Fund.

ISBN:

981238832X

OCLC:

54611297