Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists

Jürgen Fuchs, Christoph Schweigert

Cambridge University Press, Oct 7, 2003 - Mathematics - 438 pages

This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching rules, Young tableaux, spinors, Clifford algebras and supersymmetry, representations on function spaces, and Hopf algebras and representation rings. A detailed reference list is provided, and many exercises and examples throughout the book illustrate the use of Lie algebras in real physical problems. The text is written at a level accessible to graduate students, but will also provide a comprehensive reference for researchers.

Contents

• II: 1
• III: 2
• V: 3
• VI: 6
• VII: 8
• VIII: 12
• X: 14
• XI: 17
• XII: 18
• XIII: 20
• XIV: 22
• XV: 23
• XVI: 26
• XVII: 30
• XIX: 31
• XX: 32
• XXI: 36
• XXII: 38
• XXIII: 40
• XXIV: 43
• XXV: 47
• XXVI: 48
• XXVII: 51
• XXVIII: 52
• XXIX: 53
• XXX: 54
• XXXI: 57
• XXXII: 64
• XXXIV: 66
• XXXV: 68
• XXXVI: 71
• XXXVII: 73
• XXXVIII: 74
• XXXIX: 77
• XL: 82
• XLI: 84
• XLII: 86
• XLIII: 87
• XLIV: 90
• XLV: 91
• XLVI: 92
• XLVII: 95
• XLVIII: 96
• XLIX: 99
• L: 101
• LI: 102
• LII: 108
• LIII: 110
• LIV: 112
• LV: 113
• LVI: 116
• LVIII: 119
• LIX: 122
• LX: 124
• LXI: 128
• LXII: 133
• LXIII: 135
• LXIV: 136
• LXV: 139
• LXVI: 144
• LXVIII: 145
• LXIX: 147
• LXX: 149
• LXXI: 151
• LXXII: 154
• LXXIII: 156
• LXXIV: 161
• LXXV: 164
• LXXVI: 167
• LXXVII: 168
• LXXVIII: 171
• LXXIX: 172
• LXXX: 174
• LXXXI: 177
• LXXXII: 181
• LXXXIII: 183
• LXXXIV: 186
• LXXXV: 191
• LXXXVI: 192
• LXXXVII: 193
• LXXXVIII: 194
• LXXXIX: 198
• XC: 200
• XCI: 202
• XCII: 203
• XCIII: 205
• XCIV: 207
• XCV: 209
• XCVI: 211
• XCVII: 212
• XCVIII: 214
• XCIX: 215
• C: 216
• CI: 221
• CII: 222
• CIII: 225
• CIV: 228
• CV: 231
• CVI: 234
• CVII: 236
• CVIII: 237
• CIX: 238
• CX: 240
• CXI: 241
• CXII: 244
• CXIII: 245
• CXIV: 248
• CXV: 249
• CXVI: 251
• CXVII: 253
• CXVIII: 254
• CXIX: 256
• CXX: 257
• CXXI: 258
• CXXII: 261
• CXXIII: 263
• CXXIV: 266
• CXXV: 267
• CXXVI: 268
• CXXVII: 269
• CXXVIII: 271
• CXXIX: 273
• CXXXI: 276
• CXXXII: 278
• CXXXIII: 281
• CXXXIV: 286
• CXXXV: 287
• CXXXVI: 288
• CXXXVII: 291
• CXXXVIII: 294
• CXXXIX: 296
• CXL: 299
• CXLI: 301
• CXLII: 302
• CXLIII: 304
• CXLIV: 306
• CXLV: 308
• CXLVI: 309
• CXLVII: 311
• CXLVIII: 315
• CXLIX: 317
• CL: 318
• CLI: 319
• CLII: 321
• CLIII: 323
• CLIV: 326
• CLV: 330
• CLVI: 333
• CLVII: 335
• CLVIII: 337
• CLIX: 338
• CLX: 340
• CLXI: 341
• CLXII: 343
• CLXIII: 344
• CLXIV: 346
• CLXV: 347
• CLXVI: 350
• CLXVII: 353
• CLXVIII: 355
• CLXIX: 358
• CLXX: 363
• CLXXI: 364
• CLXXII: 367
• CLXXIII: 369
• CLXXIV: 370
• CLXXV: 372
• CLXXVI: 374
• CLXXVII: 375
• CLXXVIII: 378
• CLXXIX: 380
• CLXXX: 382
• CLXXXI: 386
• CLXXXII: 388
• CLXXXIII: 389
• CLXXXIV: 391
• CLXXXV: 392
• CLXXXVI: 394
• CLXXXVII: 397
• CLXXXVIII: 398
• CLXXXIX: 399
• CXC: 400
• CXCI: 402
• CXCII: 405
• CXCIII: 407
• CXCIV: 412
• CXCV: 421
• CXCVI: 430

Popular passages

Page 427 - WG McKay and J. Patera, Tables of Dimensions, Indices, and Branching Rules for Representations of Simple Lie Algebras 70.

Page 421 - AO Barut and R. Raczka, Theory of Group Representations and Applications, Second Edition, World Scientific, Singapore 1986.

Bibliographic information

• Title: Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists; Cambridge Monographs on Mathematical Physics, ISSN 0269-8242; Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists, Christoph Schweigert
• Authors: Jürgen Fuchs, Christoph Schweigert
• Edition: illustrated, reprint
• Publisher: Cambridge University Press, 2003
• ISBN: 0521541190, 9780521541190
• Length: 438 pages
• Subjects: Mathematics / Algebra / Abstract; Mathematics / Algebra / Linear; Mathematics / Group Theory; Science / Physics / General; Science / Physics / Mathematical & Computational