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9780387953113

Theoretical Physics at the End of the Twentieth Century

by ;
  • ISBN13:

    9780387953113

  • ISBN10:

    0387953116

  • Format: Hardcover
  • Copyright: 2001-12-01
  • Publisher: Springer Verlag
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Summary

This volume provides a snapshot of topics engaging theoretical physicists at the end of the twentieth century and the beginning of the twenty-first. Based on seven of the courses given at the 1999 CRM Summer School in Banff, the chapters provide timely, diverse and exciting views of their fields. The contributions include:- Supersymmetric Yang-Mills theory and integrable systems (E. D'Hoker and D.H. Phong) - Branes, black holes and anti-De Sitter space (M.J. Duff)- Turbulence (K. Gawedzki)- Bose--Einstein condensation and coherent matter waves (A. Griffin) - Deformed Virasoro and elliptic algebras (S. Odake) - Mesoscopic physics (B. Simons, A. Atland) - QCD in extreme conditions (F. Wilczek) Young physicists will find in these chapters pedagogical introductions to subjects currently active in theoretical physics, and more seasoned physicists will find a chance to share the excitement of fields outside their immediate research interests.

Table of Contents

Series Preface v
Preface vii
Contributors xvii
Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems
1(126)
Eric D'Hoker
D.H. Phong
Introduction
1(7)
Supersymmetry and the Standard Model
2(2)
Supersymmetry and Unification of Forces
4(3)
Supersymmetric Yang-Mills Dynamics
7(1)
Supersymmetric Yang-Mills in 4 Dimensions
8(20)
Supersymmetry Algebra
8(1)
Massless Particle Representations
9(1)
Massive Particle Representations
9(2)
Field Contents of Supersymmetric Field Theories
11(1)
N = 1 Supersymmetric Lagrangians
12(1)
N = 1 Superfield Methods
13(2)
Irreducible Superfields of N = 1
15(3)
General N = 1 Susy Lagrangians via Superfields
18(2)
Renormalizable N = 2,4 Susy Lagrangians
20(1)
N = 2 Superfield Methods: Unconstrained Superspace
21(3)
N = 2 Superfield Methods: Harmonic/Analytic Superspaces
24(4)
Seiberg-Witten Theory
28(19)
Wilson Effective Couplings and Actions
28(2)
Holomorphicity and Nonrenormalization
30(3)
Low Energy Dynamics of N = 2 Super-Yang-Mills
33(1)
Particle and Field Contents
34(2)
Form of the N = 2 Low Energy Effective Lagrangian
36(3)
Physical Properties of the Prepotential
39(1)
Electric-Magnetic Duality
40(2)
Monodromy via Elliptic Curves for SU (2) Gauge Group
42(2)
Physical Interpretation of Singularities
44(1)
Hypergeometric Function Representation
45(2)
More General Gauge Groups, Hypermultiplets
47(10)
Model of Riemann Surfaces
48(1)
Identifying Seiberg-Witten and Riemann Surface Data
49(1)
SU(N) Gauge Algebras, Fundamental Hypermultiplets
50(6)
Classical Gauge Algebras, Fundamental Hypermultiplets
56(1)
Mechanical Integrable Systems
57(13)
Lax Pairs with Spectral Parameter--Spectral Curves
58(1)
The Toda Systems
59(3)
The Calogero-Moser Systems for SU(N)
62(2)
Relation between Calogero-Moser and Toda for SU(N)
64(2)
Relations with KdV and KP Systems
66(1)
Calogero-Moser Systems for General Lie Algebras
67(1)
Scaling of Calogero-Moser to Toda for General Lie Algebras
68(2)
Calogero-Moser Lax Pairs for General Lie Algebras
70(17)
Lax Pairs with Spectral Parameter for Classical Lie Algebras
71(2)
The General Ansatz
73(3)
Lax Pairs for Untwisted Calogero-Moser Systems
76(6)
Lax Pairs for Twisted Calogero-Moser Systems
82(3)
Scaling Limits of Lax Pairs
85(2)
Super-Yang-Mills and Calogero-Moser Systems
87(10)
Correspondence of Seiberg-Witten and Integrable Systems
87(2)
Calogero-Moser and Seiberg-Witten Theory for SU(N)
89(1)
Four Fundamental Theorems
90(5)
Partial Decoupling of Hypermultiplet, Product Groups
95(2)
Calogero-Moser and Seiberg-Witten for General G
97(6)
The General Case
97(2)
Spectral Curves for Low Rank
99(2)
Perturbative Prepotential for SO(2n)
101(2)
References
103(10)
Notations and Conventions
113(2)
Spinors
113(1)
Dirac Matrices in a Weyl Basis
114(1)
Dirac Matrices in a Majorana Basis
114(1)
Two-Component Spinors
114(1)
Lie Algebra Theory
115(4)
Elliptic Functions
119(8)
Basic Definitions and Properties
119(3)
Half and Third Period Functions
122(1)
The Function Φ
123(1)
The Functions Λ, Φ1, Φ2
124(3)
Lectures on Branes, Black Holes, and Anti-de Sitter Space
127(118)
M.J. Duff
Introduction
127(13)
Supergravity, Supermembranes and M-Theory
127(2)
The Kaluza-Klein Idea
129(4)
The Field Content
133(4)
The AdS/CFT Correspondence
137(1)
Plan of the Lectures
138(2)
Problems 1
140(1)
Eleven-Dimensional Supergravity
140(12)
Bosonic Field Equations
140(1)
AdS4 x S7
140(4)
Consistent Truncation to the Massless Modes
144(2)
The Supermembrane Solution
146(3)
AdS7 x S4
149(1)
The Superfivebrane Solution
150(2)
Problems 2
152(1)
Type IIB Supergravity
152(3)
Bosonic Field Equations
152(1)
AdS5 x S5
153(1)
The Self-Dual Superthreebrane Solution
154(1)
Problems 3
155(1)
The M2-Brane, D3-Brane and M5-Brane
155(5)
The M2-Brane
155(2)
The M5-Brane
157(2)
The D3-Brane
159(1)
Problems 4
159(1)
ADS/CFT: The Membrane at the End of the Universe
160(14)
Singletons Live on the Boundary
160(2)
The Membrane as a Singleton: The Membrane/Supergravity Bootstrap
162(3)
Doubletons and Tripletons Revisited
165(1)
The Membrane at the End of the Universe
166(3)
Near Horizon Geometry and p-Brane Aristocracy
169(2)
Supermembranes with Fewer Supersymmetries. Skew-Whiffing
171(2)
The Maldacena Conjecture
173(1)
Problems 5
174(1)
Anti-de Sitter Black Holes
174(22)
Introduction
174(3)
S5 Reduction of Type IIB Supergravity
177(3)
D = 5 AdS Black Holes
180(1)
Rotating D3-Brane
180(3)
S7 Reduction of D = 11 Supergravity
183(3)
D = 4 AdS Black Holes
186(1)
Rotating M2-Brane
187(1)
S4 reduction of D = 11 Supergravity
188(2)
D = 7 AdS Black Holes
190(1)
Rotating M5-Brane
191(1)
Charge as Angular Momentum
192(1)
Magnetic Black Holes
193(1)
Kaluza-Klein States as Black Holes
194(1)
Recent Developments
195(1)
Problems 6
196(1)
Solutions to Problems
196(16)
Solutions 1
196(2)
Solutions 2
198(3)
Solutions 3
201(3)
Solutions 4
204(2)
Solutions 5
206(1)
Solutions 6
207(5)
References
212(16)
The Lagrangian, Symmetries and Transformation Rules of D = 11 Supergravity
228(2)
The Field Equations, Symmetries and Transformation Rules of Type IIB Supergravity
230(3)
The Lagrangian, Symmetries and Transformation Rules of the M2-Brane
233(1)
The Field Equations, Symmetries and Transformation Rules of the M5-Brane
234(4)
The Lagrangian, Symmetries and Transformation Rules of the D3-Brane
238(2)
D = 4, N = 2 Gauged Supergravity
240(5)
Easy Turbulence
245(32)
Krzysztof Gawedzki
Lecture 1 The Navier-Stokes Equations
245(7)
Lecture 2 The Kolmogorov and Kraichnan-Batchelor Theories of Turbulence
252(7)
Lecture 3 The Richardson Dispersion Law
259(8)
Weakly Compressible Regime
265(1)
Strongly Compressible Regime
265(2)
Lecture 4 Cascades and Intermittency
267(10)
BEC and the New World of Coherent Matter Waves
277(30)
Allan Griffin
An Overview of Past and Recent Work
278(7)
Some History before 1980
278(3)
More Recent Developments (1980-1995)
281(4)
Dynamics of the Pure Condensate
285(9)
Static Condensate
287(2)
Dynamics of the Condensate (Collective Modes)
289(2)
Quantum Hydrodynamic Formulation
291(2)
Interference of Coherent Matter Waves
293(1)
Coupled Dynamics of the Condensate and Noncondensate
294(9)
References
303(4)
Beyond CFT: Deformed Virasoro and Elliptic Algebras
307(144)
Satoru Odake
Introduction
307(3)
Conformal Field Theory and Virasoro Algebra
310(24)
Conformal Field Theory
310(1)
Virasoro Algebra
310(8)
Free Field Realization
318(16)
Deformed Virasoro Algebra (A1(1) Type)
334(21)
Definition and Consistency
334(3)
Conformal Limit
337(1)
Representation Theory
338(2)
Free Field Realization
340(13)
Higher DVA Currents
353(2)
Solvable Lattice Models and Elliptic Algebras
355(35)
Solvable Lattice Models and Yang-Baxter Equation
355(4)
Corner Transfer Matrices and Vertex Operators
359(14)
Introduction to Quasi-Hopf Algebra
373(5)
Elliptic Quantum Groups
378(12)
Free Field Approach to ABF Model
390(22)
ABF Model
391(2)
Vertex Operators
393(6)
Local Height Probability
399(4)
Form Factor
403(4)
OPE and Trace
407(2)
Screening Operators and Vertex Operators
409(3)
DVA (A2(2) Type) and Dilute AL Models
412(18)
DVA (A2(2))
412(2)
Free Field Realization
414(4)
Dilute AL Models
418(2)
Free Field Approach
420(8)
OPE and trace
428(2)
Conclusion
430(3)
References
433(8)
Some Formulas
441(10)
Some Functions
442(1)
Delta Function
443(1)
Some Summations
444(1)
Some Integrals
445(2)
Hausdorff Formula
447(1)
Trace Technique
447(4)
Mesoscopic Physics
451(116)
B.D. Simons
A. Altland
Introduction to Mesoscopic Physics
451(31)
Manifestations of Phase Coherence in Mesoscopics
454(5)
Qualitative Considerations: Feynman Paths
459(14)
Interaction Phenomena
473(7)
Impurity Diagram Technique
480(2)
Field Theory of Disordered Conductors
482(15)
Derivation of the σ-Model Action
484(8)
Applications of the σ-Model
492(4)
Random Matrix Theory
496(1)
Quantum Chaos
497(17)
Spectral Statistics: A Brief History
500(3)
Semi-Classics and the Trace Formula
503(3)
Ballistic σ-Model
506(1)
Perturbation Theory
506(3)
Quantum Hall Effect
509(5)
Coulomb Interaction Phenomena
514(12)
Matsubara Field Integral
515(3)
Plasma Theory of the Free Electron Gas
518(3)
Plasma Theory of the Disordered Electron Gas
521(2)
Gauge Fixing: Low-Energy Saddle-Point
523(1)
Zero-Bias Anomaly
524(2)
Novel Symmetry Classes
526(32)
Realizations of Novel Symmetries
529(2)
Dirty Superconductivity
531(5)
Hybrid Superconductor-Normal Systems
536(6)
Dirty d-Wave Superconductivity
542(1)
Chiral Symmetry and Sublattice Models
543(9)
Random Classical Dynamics
552(6)
References
558(9)
QCD In Extreme Conditions
567
Frank Wilczek
Introduction
567
Symmetry and the Phenomena of QCD
569
Apparent and Actual Symmetries
569
Asymptotic Freedom
572
Confinement
577
Chiral Symmetry Breaking
583
Chiral Anomalies and Instantons
587
High Temperature QCD: Asymptotic Properties
592
Significance of High Temperature QCD
592
Numerical Indications for Quasi-Free Behavior
593
Ideas About Quark-Gluon Plasma
594
Screening Versus Confinement
596
Models of Chiral Symmetry Breaking
598
More Refined Numerical Experiments
601
High-Temperature QCD: Phase Transitions
603
Yoga of Phase Transitions and Order Parameters
603
Application to Glue Theories
607
Application to Chiral Transitions
608
Close Up on Two Flavors
611
A Genuine Critical Point! (?)
615
High-Density QCD: Methods
618
Hopes, Doubts, and Fruition
618
Another Renormalization Group
620
Pairing Theory
621
Taming the Magnetic Singularity
623
High-Density QCD: Color-Flavor Locking and Quark-Hadron Continuity
624
Gauge Symmetry (Non)Breaking
625
Symmetry Accounting
626
Elementary Excitations
628
A Modified Photon
629
Quark-Hadron Continuity
630
Remembrance of Things Past
630
More Quarks
631
Fewer Quarks, and Reality
631

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