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Aspects of Symmetry : Selected Erice Lectures - Sidney Coleman

Aspects of Symmetry

Selected Erice Lectures

Paperback Published: 18th April 1988
ISBN: 9780521318273
Number Of Pages: 420

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This collection of review lectures on topics in theoretical high energy physics has few rivals for clarity of exposition and depth of insight. Delivered over the past two decades at the International School of Subnuclear Physics in Erice, Sicily, the lectures help to organize and explain material that a the time existed in a confused state, scattered in the literature. At the time they were given they spread new ideas throughout the physics community and proved very popular as introductions to topics at the frontiers of research.

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Prefacep. xiii
Acknowledgementsp. xiv
An introduction to unitary symmetry
The search for higher symmetriesp. 1
The eight-baryon puzzlep. 1
The elimination of G[subscript 0]p. 4
SU(3) and its representationsp. 5
The representations of SU(n)p. 5
The representations of SU(2)p. 6
The representations of SU(3)p. 7
Dimensions of the IRsp. 8
Isospin and hyperchargep. 9
Isospin-hypercharge decompositionsp. 10
The Clebsch-Gordan seriesp. 12
Some theoremsp. 15
Invariant couplingsp. 17
The problem of Cartesian componentsp. 17
SU(2) againp. 18
SU(3) octets: trilinear couplingsp. 19
A mixed notationp. 21
Applicationsp. 23
Electromagnetismp. 23
Magnetic moments: baryonsp. 24
Electromagnetic mass splittingsp. 25
Electromagnetic properties of the decupletp. 26
The medium-strong interactionsp. 26
Ideas of octet enhancementp. 28
Bibliographyp. 35
Soft pions
The reduction formulap. 36
The weak interactions: first principlesp. 40
The Goldberger-Treiman relation and a first glance at PCACp. 41
A hard look at PCACp. 42
The gradient-coupling modelp. 45
Adler's rule for the emission of one soft pionp. 47
Current commutatorsp. 50
Vector-vector commutatorsp. 50
Vector-axial commutatorsp. 51
Axial-axial commutatorsp. 51
The Weinberg-Tomozawa formula and the Adler-Weisberger relationp. 52
Pion-pion scattering a la Weinbergp. 57
Kaon decaysp. 60
Notational conventionsp. 63
No-renormalization theoremp. 63
Threshold S-matrix and threshold scattering lengthsp. 64
Bibliographyp. 65
Introductionp. 67
The formal theory of broken scale invariancep. 68
Symmetries, currents, and Ward identitiesp. 68
Scale transformations and scale dimensionsp. 70
More about the scale current and a quick look at the conformal groupp. 71
Hidden scale invariancep. 76
The death of scale invariancep. 79
Some definitions and technical detailsp. 79
A disaster in the deep Euclidean regionp. 80
Anomalous dimensions and other anomaliesp. 82
The last anomalies: the Callan-Symanzik equationsp. 84
The resurrection of scale invariancep. 88
The renormalization group equations and their solutionp. 88
The return of scaling in the deep Euclidean regionp. 90
Scaling and the operator product expansionp. 93
Conclusions and questionsp. 96
Notes and referencesp. 97
Renormalization and symmetry: a review for non-specialists
Introductionp. 99
Bogoliubov's method and Hepp's theoremp. 99
Renormalizable and non-renormalizable interactionsp. 104
Symmetry and symmetry-breaking: Symanzik's rulep. 106
Symmetry and symmetry-breaking: currentsp. 108
Notes and referencesp. 111
Secret symmetry: an introduction to spontaneous symmetry breakdown and gauge fields
Introductionp. 113
Secret symmetries in classical field theoryp. 115
The idea of spontaneous symmetry breakdownp. 115
Goldstone bosons in an Abelian modelp. 118
Goldstone bosons in the general casep. 119
The Higgs phenomenon in the Abelian modelp. 121
Yang-Mills fields and the Higgs phenomenon in the general casep. 124
Summary and remarksp. 126
Secret renormalizabilityp. 128
The order of the argumentsp. 128
Renormalization reviewedp. 128
Functional methods and the effective potentialp. 132
The loop expansionp. 135
A sample computationp. 136
The most important part of this lecturep. 138
The physical meaning of the effective potentialp. 139
Accidental symmetry and related phenomenap. 142
An alternative method of computationp. 144
Functional integration (vulgarized)p. 145
Integration over infinite-dimensional spacesp. 145
Functional integrals and generating functionalsp. 148
Feynman rulesp. 152
Derivative interactionsp. 154
Fermi fieldsp. 156
Ghost fieldsp. 158
The Feynman rules for gauge field theoriesp. 159
Troubles with gauge invariancep. 159
The Faddeev-Popov Ansatzp. 160
The application of the Ansatzp. 163
Justification of the Ansatzp. 165
Concluding remarksp. 167
Asymptotic freedomp. 169
Operator products and deep inelastic electroproductionp. 169
Massless field theories and the renormalization groupp. 171
Exact and approximate solutions of the renormalization group equationsp. 174
Asymptotic freedomp. 176
No conclusionsp. 179
One-loop effective potential in the general casep. 180
Notes and referencesp. 182
Classical lumps and their quantum descendants
Introductionp. 185
Simple examples and their propertiesp. 187
Some time-independent lumps in one space dimensionp. 187
Small oscillations and stabilityp. 191
Lumps are like particles (almost)p. 192
More dimensions and a discouraging theoremp. 194
Topological conservation lawsp. 195
The basic idea and the main resultsp. 195
Gauge field theories revisitedp. 198
Topological conservation laws, or, homotopy classesp. 202
Three examples in two spatial dimensionsp. 205
Three examples in three dimensionsp. 208
Patching together distant solutions, or, homotopy groupsp. 209
Abelian and non-Abelian magnetic monopoles, or, [Pi][subscript 2](G/H) as a subgroup of [Pi][subscript 1](H)p. 215
Quantum lumpsp. 223
The nature of the classical limitp. 223
Time-independent lumps: power-series expansionp. 225
Time-independent lumps: coherent-state variational methodp. 232
Periodic lumps: the old quantum theory and the DHN formulap. 239
A very special systemp. 246
A curious equivalencep. 246
The secret of the solitonp. 250
Qualitative and quantitative knowledgep. 252
Some opinionsp. 253
A three-dimensional scalar theory with non-dissipative solutionsp. 254
A theorem on gauge fieldsp. 256
A trivial extensionp. 257
Looking for solutionsp. 257
Singular and non-singular gauge fieldsp. 259
Notes and referencesp. 262
The uses of instantons
Introductionp. 265
Instantons and bounces in particle mechanicsp. 268
Euclidean functional integralsp. 268
The double well and instantonsp. 270
Periodic potentialsp. 277
Unstable states and bouncesp. 278
The vacuum structure of gauge field theoriesp. 282
Old stuffp. 282
The winding numberp. 284
Many vacuap. 291
Instantons: generalitiesp. 295
Instantons: particularsp. 297
The evaluation of the determinant and an infrared embarrassmentp. 300
The Abelian Higgs model in 1 + 1 dimensionsp. 302
't Hooft's solution of the U(1) problemp. 307
The mystery of the missing mesonp. 307
Preliminaries: Euclidean Fermi fieldsp. 311
Preliminaries: chiral Ward identitiesp. 314
QCD (baby version)p. 316
QCD (the real thing)p. 323
Miscellanyp. 324
The fate of the false vacuump. 327
Unstable vacuap. 327
The bouncep. 329
The thin-wall approximationp. 332
The fate of the false vacuump. 334
Determinants and renormalizationp. 336
Unanswered questionsp. 339
How to compute determinantsp. 340
The double well done doubly wellp. 341
Finite action is zero measurep. 344
Only winding number survivesp. 345
No wrong-chirality solutionsp. 347
Notes and referencesp. 348
Introductionp. 351
Vector representations, or, soluble modelsp. 352
[phi][superscript 4] theory (half-way)p. 352
The Gross-Neveu modelp. 358
The CP[superscript N - 1] modelp. 362
Adjoint representations, or, chromodynamicsp. 368
The double-line representation and the dominance of planar graphsp. 368
Topology and phenomenologyp. 373
The 't Hooft modelp. 378
Witten's theory of baryonsp. 386
The master fieldp. 391
Restrospect and prospectp. 396
The Euler characteristicp. 397
The 't Hooft equationsp. 398
U(N) as an approximation to SU(N)p. 400
Notes and referencesp. 401
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521318273
ISBN-10: 0521318270
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 420
Published: 18th April 1988
Country of Publication: GB
Dimensions (cm): 22.81 x 15.55  x 2.67
Weight (kg): 0.62