GROUP-THEORETICAL METHODS IN PHYSICS
CONTENTS THE ELEMENTARY PROPERTIES OF GROUPS 11 DEFINITIONS 12 CONJUGATE ELEMENTS AND CLASSES 13 SUBGROUPS AND COSETS 14 THE FACTOR GROUP 16 PRODUCT GROUPS 17 MAPPINGS, HOMOMORPHISMS, AND EXTENSIONS 18 MORE ABOUT SUBGROUPS AND CLASSES PROBLEMS SYMMETRY OPERATORS AND POINT GROUPS 21 DEFINITIONS 22 THE MULTIPLICATION TABLE – AN EXAMPLE 23 THE SYMMETRY POINT GROUPS 24 IDENTIFICATION OF MOLECULAR POINT GROUPS MATRIX REPRESENTATIVES 31 LINEAR VECTOR SPACES 32 MATRIX REPRESENTATIVES OF OPERATORS 33 MAPPINGS 34 GROUP REPRESENTATIONS 35 TRANSFORMATION OF FUNCTIONS 36 SOME QUANTUM MECHANICAL CONSIDERATIONS GROUP REPRESENTATIONS 41 MATRIX REPRESENTATIONS 42 IRREDUCIBLE REPRESENTATIONS 43 THE ORTHOGONALITY THEOREM 44 THE CHARACTERS OF A REPRESENTATION 45 CHARACTER TABLES 46 AXIAL VECTORS 47 CYCLIC GROUPS 48 INDUCED REPRESENTATIONS BASES OF REPRESENTATIONS 51 BASIS FUNCTIONS 52 CONSTRUCTION OF BASIS FUNCTIONS 53 DIRECT PRODUCT REPRESENTATIONS 54 MATRIX ELEMENTS MOLECULAR ORBITALS 61 HYBRIDIZATION 62 P ELECTRON SYSTEMS 63 EQUIVALENT BOND ORBITALS 64 TRANSITION METAL COMPLEXES CRYSTAL-FIELD THEORY 71 ELECTRON SPIN 72 SPHERICAL SYMMETRY 73 INTERMEDIATE CRYSTAL FIELD 74 STRONG CRYSTAL FIELDS DOUBLE GROUPS 81 SPIN–ORBIT COUPLING AND DOUBLE GROUPS 82 WEAK CRYSTAL FIELDS MOLECULAR VIBRATIONS 91 CLASSIFICATION OF NORMAL MODES 92 ALLOWED TRANSITIONS 93 INELASTIC RAMAN SCATTERING 94 DETERMINATION OF THE NORMAL MODES TRANSITIONS BETWEEN ELECTRONIC STATES 101 SELECTION RULES 102 VIBRONIC COUPLING 103 CHARGE TRANSFER CONTINUOUS GROUPS 112 THE INFINITESIMAL GENERATOR FOR SO(2) 114 THE COMMUTATION RELATIONS 115 THE IRREDUCIBLE REPRESENTATIONS OF SO(3) 116 THE SPECIAL UNITARY GROUP SU(2) 117 EULER PARAMETERIZATION OF A ROTATION 118 THE HOMOMORPHISM OF SU(2) AND SO(3) PROJECTIVE REPRESENTATIONS 121 COMPLEX NUMBERS 122 QUATERNIONS 123 GEOMETRY OF ROTATIONS 124 THE THEORY OF TURNS 125 THE ALGEBRA OF TURNS 126 PROJECTIVE REPRESENTATIONS 127 IMPROPER GROUPS 128 THE IRREDUCIBLE REPRESENTATIONS TIME-REVERSAL SYMMETRY 131 TIME EVOLUTION 132 TIME REVERSAL WITH NEGLECT OF ELECTRON SPIN 133 TIME REVERSAL WITH SPIN–ORBIT COUPLING 134 CO-REPRESENTATIONS MAGNETIC POINT GROUPS 141 CRYSTALLOGRAPHIC MAGNETIC POINT GROUPS 142 CO-REPRESENTATIONS OF MAGNETIC POINT GROUPS 143 CLEBSCH–GORDAN COEFFICIENTS 144 CRYSTAL-FIELD THEORY FOR MAGNETIC CRYSTALS PHYSICAL PROPERTIES OF CRYSTALS 151 TENSORS 152 CRYSTAL SYMMETRY: THE DIRECT METHOD 153 GROUP THEORY AND PHYSICAL PROPERTIES OF CRYSTALS 154 APPLICATIONS 155 PROPERTIES OF CRYSTALS WITH MAGNETIC POINT GROUPS SPACE GROUPS 161 TRANSLATIONAL SYMMETRY 162 THE SPACE GROUP OF A CRYSTAL 163 RECIPROCAL LATTICE AND BRILLOUIN ZONES 164 SPACE-GROUP REPRESENTATIONS 165 THE COVERING GROUP 166 THE IRREDUCIBLE REPRESENTATIONS OF G 167 HERRING METHOD FOR NON-SYMMORPHIC SPACE GROUPS 168 SPINOR REPRESENTATIONS OF SPACE GROUPS ELECTRONIC ENERGY STATES IN CRYSTALS 171 TRANSLATIONAL SYMMETRY 172 TIME-REVERSAL SYMMETRY 173 TRANSLATIONAL SYMMETRY IN THE RECIPROCAL LATTICE REPRESENTATION 174 POINT GROUP SYMMETRY 175 ENERGY BANDS IN THE FREE-ELECTRON APPROXIMATION: SYMMORPHIC SPACE GROUPS 176 FREE-ELECTRON STATES FOR CRYSTALS WITH NON-SYMMORPHIC SPACE GROUPS 177 SPINOR REPRESENTATIONS 178 TRANSITIONS BETWEEN ELECTRONIC STATES VIBRATION OF ATOMS IN CRYSTALS 181 EQUATIONS OF MOTION 182 SPACE-GROUP SYMMETRY 183 SYMMETRY OF THE DYNAMICAL MATRIX 184 SYMMETRY COORDINATES 185 TIME-REVERSAL SYMMETRY 186 AN EXAMPLE: SILICON