Symmetry: An Introduction to Group Theory and Its ApplicationsElsevier, 3 sept. 2013 - 262 pages Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students. |
Table des matières
| 1 | |
CHAPTER 2 LATTICES AND VECTOR SPACES | 22 |
CHAPTER 3 POINT AND SPACE GROUPS | 54 |
CHAPTER 4 REPRESENTATIONS OF POINT AND TRANSLATION GROUPS | 91 |
CHAPTER 5 IRREDUCIBLE REPRESENTATIONS | 109 |
CHAPTER 6 APPLICATIONS INVOLVING ALGEBRAIC FORMS | 140 |
CHAPTER 7 APPLICATIONS INVOLVING FUNCTIONS AND OPERATORS | 166 |
CHAPTER 8 APPLICATIONS INVOLVING TENSORS AND TENSOR OPERATORS | 203 |
Representations carried by harmonic functions | 235 |
Alternative bases for cubic groups | 241 |
| 245 | |
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Expressions et termes fréquents
3-dimensional algebra angle associated atom axes basic basis vectors block form Cartesian chapter character system coefficients collection column commutative consider contains contravariant coordinates corresponding coset crystal defined degenerate denote described diagonal dimensions direct product displacement eigenvectors equivalent example field finite group follows geometrical give given group C3 group elements group G group theory hence holohedry identity improper rotation indicated invariant inverse irreducible representations isomorphic lattice law of combination linear combinations mapping matrix element modes molecular molecule multiplication table normal notation obtain orbitals orthogonal orthorhombic physical plane point group operation principal axis projection quantities quantum mechanics reduced reflection representation carried result rotation group scalar product self-coincidence space groups subgroup subspace symmetry adapted symmetry functions symmetry group symmetry operations symmetry species symmetry vectors tation tensor operators tensorial set theorem translation types unitary unitary matrix vector components vector space vibration zero