Aspects of Symmetry Selected Erice Lectures

ISBN-10: 0521318270

ISBN-13: 9780521318273

Edition: 1988

Authors: Sidney Coleman

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Description:

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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Book details

List price: $62.00
Copyright year: 1988
Publisher: Cambridge University Press
Publication date: 2/18/1988
Binding: Paperback
Pages: 420
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.100
Language: English

Preface
Acknowledgements
An introduction to unitary symmetry
The search for higher symmetries
The eight-baryon puzzle
The elimination of G[subscript 0]
SU(3) and its representations
The representations of SU(n)
The representations of SU(2)
The representations of SU(3)
Dimensions of the IRs
Isospin and hypercharge
Isospin-hypercharge decompositions
The Clebsch-Gordan series
Some theorems
Invariant couplings
The problem of Cartesian components
SU(2) again
SU(3) octets: trilinear couplings
SU(3) OCTETS: QUADRILINEAR COUPLINGS
A mixed notation
Applications
Electromagnetism
Magnetic moments: baryons
Electromagnetic mass splittings
Electromagnetic properties of the decuplet
The medium-strong interactions
Ideas of octet enhancement
Bibliography
Soft pions
The reduction formula
The weak interactions: first principles
The Goldberger-Treiman relation and a first glance at PCAC
A hard look at PCAC
The gradient-coupling model
Adler's rule for the emission of one soft pion
Current commutators
Vector-vector commutators
Vector-axial commutators
Axial-axial commutators
The Weinberg-Tomozawa formula and the Adler-Weisberger relation
Pion-pion scattering a la Weinberg
Kaon decays
Notational conventions
No-renormalization theorem
Threshold S-matrix and threshold scattering lengths
Bibliography
Dilatations
Introduction
The formal theory of broken scale invariance
Symmetries, currents, and Ward identities
Scale transformations and scale dimensions
More about the scale current and a quick look at the conformal group
Hidden scale invariance
The death of scale invariance
Some definitions and technical details
A disaster in the deep Euclidean region
Anomalous dimensions and other anomalies
The last anomalies: the Callan-Symanzik equations
The resurrection of scale invariance
The renormalization group equations and their solution
The return of scaling in the deep Euclidean region
Scaling and the operator product expansion
Conclusions and questions
Notes and references
Renormalization and symmetry: a review for non-specialists
Introduction
Bogoliubov's method and Hepp's theorem
Renormalizable and non-renormalizable interactions
Symmetry and symmetry-breaking: Symanzik's rule
Symmetry and symmetry-breaking: currents
Notes and references
Secret symmetry: an introduction to spontaneous symmetry breakdown and gauge fields
Introduction
Secret symmetries in classical field theory
The idea of spontaneous symmetry breakdown
Goldstone bosons in an Abelian model
Goldstone bosons in the general case
The Higgs phenomenon in the Abelian model
Yang-Mills fields and the Higgs phenomenon in the general case
Summary and remarks
Secret renormalizability
The order of the arguments
Renormalization reviewed
Functional methods and the effective potential
The loop expansion
A sample computation
The most important part of this lecture
The physical meaning of the effective potential
Accidental symmetry and related phenomena
An alternative method of computation
Functional integration (vulgarized)
Integration over infinite-dimensional spaces
Functional integrals and generating functionals
Feynman rules
Derivative interactions
Fermi fields
Ghost fields
The Feynman rules for gauge field theories
Troubles with gauge invariance
The Faddeev-Popov Ansatz
The application of the Ansatz
Justification of the Ansatz
Concluding remarks
Asymptotic freedom
Operator products and deep inelastic electroproduction
Massless field theories and the renormalization group
Exact and approximate solutions of the renormalization group equations
Asymptotic freedom
No conclusions
One-loop effective potential in the general case
Notes and references
Classical lumps and their quantum descendants
Introduction
Simple examples and their properties
Some time-independent lumps in one space dimension
Small oscillations and stability
Lumps are like particles (almost)
More dimensions and a discouraging theorem
Topological conservation laws
The basic idea and the main results
Gauge field theories revisited
Topological conservation laws, or, homotopy classes
Three examples in two spatial dimensions
Three examples in three dimensions
Patching together distant solutions, or, homotopy groups
Abelian and non-Abelian magnetic monopoles, or, [Pi][subscript 2](G/H) as a subgroup of [Pi][subscript 1](H)
Quantum lumps
The nature of the classical limit
Time-independent lumps: power-series expansion
Time-independent lumps: coherent-state variational method
Periodic lumps: the old quantum theory and the DHN formula
A very special system
A curious equivalence
The secret of the soliton
Qualitative and quantitative knowledge
Some opinions
A three-dimensional scalar theory with non-dissipative solutions
A theorem on gauge fields
A trivial extension
Looking for solutions
Singular and non-singular gauge fields
Notes and references
The uses of instantons
Introduction
Instantons and bounces in particle mechanics
Euclidean functional integrals
The double well and instantons
Periodic potentials
Unstable states and bounces
The vacuum structure of gauge field theories
Old stuff
The winding number
Many vacua
Instantons: generalities
Instantons: particulars
The evaluation of the determinant and an infrared embarrassment
The Abelian Higgs model in 1 + 1 dimensions
't Hooft's solution of the U(1) problem
The mystery of the missing meson
Preliminaries: Euclidean Fermi fields
Preliminaries: chiral Ward identities
QCD (baby version)
QCD (the real thing)
Miscellany
The fate of the false vacuum
Unstable vacua
The bounce
The thin-wall approximation
The fate of the false vacuum
Determinants and renormalization
Unanswered questions
How to compute determinants
The double well done doubly well
Finite action is zero measure
Only winding number survives
No wrong-chirality solutions
Notes and references
1/N
Introduction
Vector representations, or, soluble models
[phi][superscript 4] theory (half-way)
The Gross-Neveu model
The CP[superscript N - 1] model
Adjoint representations, or, chromodynamics
The double-line representation and the dominance of planar graphs
Topology and phenomenology
The 't Hooft model
Witten's theory of baryons
The master field
Restrospect and prospect
The Euler characteristic
The 't Hooft equations
U(N) as an approximation to SU(N)
Notes and references
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