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1.

図書

図書
edited by Gerard 't Hooft ... [et al.]
出版情報: New York : Plenum Press, c1997  viii, 373 p. ; 26 cm
シリーズ名: NATO ASI series ; Series B . Physics ; v. 364
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2.

図書

図書
Henrik Aratyn ... [et al.] (eds.)
出版情報: Berlin ; New York : Springer, c1998  xi, 379 p. ; 24 cm
シリーズ名: Lecture notes in physics ; 502
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3.

図書

図書
editors, H. -D. Doebner, P. Nattermann, W. Scherer
出版情報: Singapore : World Scientific, 1997  2 v. ; 24 cm
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4.

図書

図書
Michel C. Delfour, editor
出版情報: Providence, RI : American Mathematical Society, c1998  xii, 343 p. ; 26 cm
シリーズ名: CRM proceedings & lecture notes ; v. 13
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The transition to turbulence via turbulent bursts / K. Coughlin
Intrinsic differential geometric methods in the asymptotic analysis of linear thin shells / M. C. Delfour
Shape analysis via distance functions: Local theory / J.-P. Zolesio.
Six lectures on shape memory / I. Muller
Six lectures on superconductivity / J. Rubinstein
Front propagation / H. M. Soner
Six talks on hysteresis / A. Visintin
Dynamic metastability and singular perturbations / M. J. Ward
Dendrites, fingers, interfaces and free boundaries / J.-J. Xu
The transition to turbulence via turbulent bursts / K. Coughlin
Intrinsic differential geometric methods in the asymptotic analysis of linear thin shells / M. C. Delfour
Shape analysis via distance functions: Local theory / J.-P. Zolesio.
5.

図書

図書
édité par A. Connes, K. Gawedzki, et J. Zinn-Justin
出版情報: Amsterdam ; Tokyo : Elsevier Science, c1998  xxxvii, 990 p. ; 23 cm
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Lecturers
Seminar Speakers
Participants
Preface (French)
Preface (English)
Mathematics / Part I.:
Fields, Strings and Duality / R. DijkgraafCourse 1.:
Introduction / 1.:
What is a quantum field theory? / 2.:
Axioms vs. path-integrals / 2.1.:
Duality / 2.2.:
Quantum mechanics / 3.:
Supersymmetric quantum mechanics / 3.1.:
Quantum mechanics and perturbative field theory / 3.2.:
Two-dimensional topological field theory / 4.:
Axioms of topological field theory / 4.1.:
Topological field theory in two dimensions / 4.2.:
Example - quantum cohomology / 4.3.:
Riemann surfaces and moduli / 5.:
The moduli space of curves / 5.1.:
Example - genus one / 5.2.:
Surfaces with punctures / 5.3.:
The stable compactification / 5.4.:
Conformal field theory / 6.:
Algebraic approach / 6.1.:
Functorial approach / 6.2.:
Free bosons / 6.3.:
Free fermions / 6.4.:
Sigma models and T-duality / 7.:
Two-dimensional sigma models / 7.1.:
Toroidal models / 7.2.:
Intermezzo - lattices / 7.3.:
Spectrum and moduli of toroidal models / 7.4.:
The two-torus / 7.5.:
Path-integral computation of the partition function / 7.6.:
Supersymmetric sigma models and Calabi-Yau spaces / 7.7.:
Calabi-Yau moduli space and special geometry / 7.8.:
Perturbative string theory / 8.:
Axioms for string vacua / 8.1.:
Intermezzo - twisting and supersymmetry / 8.2.:
Example - The critical bosonic string / 8.3.:
Example - Twisted N = 2 SCFT / 8.4.:
Example - twisted minimal model / 8.5.:
Example - topological string / 8.6.:
Functorial definition / 8.7.:
Tree-level amplitudes / 8.8.:
Families of string vacua / 8.9.:
The Gauss-Manin connection / 8.10.:
Anti-holomorphic dependence and special geometry / 8.11.:
Local special geometry / 8.12.:
Gauge theories and S-duality / 9.:
Introduction to four-dimensional geometry / 9.1.:
The Lorentz group / 9.2.:
Duality in Maxwell theory / 9.3.:
The partition function / 9.4.:
Higher rank groups / 9.5.:
Dehn twists and monodromy / 9.6.:
Moduli spaces / 10.:
Supersymmetric or BPS configurations / 10.1.:
Localization in topological field theories / 10.2.:
Quantization / 10.3.:
Families of QFTs / 10.4.:
Moduli spaces of vacua / 10.5.:
Supersymmetric gauge theories / 11.:
Twisting and Donaldson theory / 11.1.:
Observables / 11.3.:
Abelian models / 11.4.:
Rigid special geometry / 11.5.:
Families of abelian varieties / 11.6.:
BPS states / 11.7.:
Non-abelian N = 2 gauge theory / 11.8.:
The Seiberg-Witten solution / 11.9.:
Physical interpretation of the singularities / 11.10.:
Implications for four-manifold invariants / 11.11.:
String vacua / 12.:
Perturbative string theories / 12.1.:
IIA or IIB / 12.2.:
D-branes / 12.3.:
Compactification / 12.4.:
Singularities revisited / 12.5.:
String moduli spaces / 12.6.:
Example - Type II on T[superscript 6] / 12.7.:
BPS states and D-branes / 13.:
Perturbative string states / 13.1.:
Perturbative BPS states / 13.2.:
D-brane states / 13.3.:
Example - Type IIA on K3 = Heterotic on T[superscript 4] / 13.4.:
Example - Type II on T[superscript 4] / 13.5.:
Example - Type II on K3 [times] S[superscript 1] = Heterotic on T[superscript 5] / 13.6.:
Example - Type IIA on X = Type IIB on Y / 13.7.:
References
How the Algebraic Bethe Ansatz Works for Integrable Models / L.D. FaddeevCourse 2.:
General outline of the course
XXX[subscript 1/2] model. Description
XXX[subscript 1/2] model. Bethe Ansatz equations
XXX[subscript 1/2] model. Physical spectrum in the ferromagnetic thermodynamic limit
XXX[subscript 1/2] model. BAE for an arbitrary configuration
XXX[subscript 1/2] model. Physical spectrum in the antiferromagnetic case
XXX[subscript s] model
XXX[subscript s] spin chain. Applications to the physical systems
XXZ model
Inhomogeneous chains and discrete time shift
Examples of dynamical models in discrete space-time
Conclusions and perspectives
Comments on the literature on BAE / 14.:
Supersymmetric Quantum Theory, Non-Commutative Geometry, and Gravitation / J. Frohlich ; O. Grandjean ; A. RecknagelCourse 3.:
The classical theory of gravitation
(Non-relativistic) quantum theory
Reconciling quantum theory with general relativity: quantum space-time-matter
Classical differential topology and -geometry and supersymmetric quantum theory
Pauli's electron
The special case where M is a Lie group
Supersymmetric quantum theory and geometry put into perspective
Supersymmetry and non-commutative geometry
Spin[superscript c] non-commutative geometry
The spectral data of spin[superscript c] NCG / 5.1.1.:
Differential forms / 5.1.2.:
Integration / 5.1.3.:
Vector bundles and Hermitian structures / 5.1.4.:
Generalized Hermitian structure on [Omega superscript k](A) / 5.1.5.:
Connections / 5.1.6.:
Riemannian curvature and torsion / 5.1.7.:
Generalized Kahler non-commutative geometry and higher supersymmetry / 5.1.8.:
Aspects of the algebraic topology of N = n supersymmetric spectral data / 5.1.9.:
Non-commutative Riemannian geometry
N = (1, 1) supersymmetry and Riemannian geometry / 5.2.1.:
Unitary connections and scalar curvature / 5.2.2.:
Remarks on the relation between N = 1 and N = (1, 1) spectral data / 5.2.5.:
Riemannian and spin[superscript c] "manifolds" in non-commutative geometry / 5.2.6.:
Algebraic topology of N = [characters not reproducible] spectral data / 5.2.7.:
Central extensions of supersymmetry, and equivariance / 5.2.8.:
N = (n, n) supersymmetry, and supersymmetry breaking / 5.2.9.:
Reparametrization invariance, BRST cohomology, and target space supersymmetry
The non-commutative torus
Spin geometry (N = 1) / 6.1:
Integration and Hermitian structure over [Omega superscript 1 subscript D](A[alpha]) / 6.1.1.:
Connections on [Omega superscript 1 subscript D](A[alpha]) / 6.1.3.:
Riemannian geometry (N = [characters not reproducible]
Kahler geometry (N = [characters not reproducible]
Applications of non-commutative geometry to quantum theories of gravitation
From point-particles to strings
A Schwinger-Dyson equation for string Green functions from reparametrization invariance and world-sheet supersymmetry
Some remarks on M(atrix) models
Two-dimensional conformal field theories
Recap of two-dimensional, local quantum field theory / 7.4.1.:
A dictionary between conformal field theory and Lie group theory / 7.4.2.:
Reconstruction of (non-commutative) target spaces from conformal field theory
Superconformal field theories, and the topology of target spaces
The N = 1 super-Virasoro algebra / 7.6.1.:
N = 2 and N = 4 supersymmetry; mirror symmetry / 7.6.2.:
Conclusions
Lectures on the Quantum Geometry of String Theory / B.R. GreeneCourse 4.:
What is quantum geometry? / 1.1.:
The ingredients / 1.2.:
The N = 2 superconformal algebra
The algebra
Representation theory of the N = 2 superconformal algebra
Chiral primary fields / 2.3.:
Spectral flow and the U(1) projection / 2.4.:
Four examples / 2.5.:
Example one: free field theory / 2.5.1.:
Example two: nonlinear sigma models / 2.5.2.:
Example three: Landau-Ginzburg models / 2.5.3.:
Example four: minimal models / 2.5.4.:
Families of N = 2 theories
Marginal operators
Moduli spaces: I
Interrelations between various N = 2 superconformal theories
Landau-Ginzburg theories and minimal models
Minimal models and Calabi-Yau manifolds: a conjectured correspondence
Arguments establishing minimal-model/Calabi-Yau correspondence
Mirror manifolds
Strategy of the construction
Minimal models and their automorphisms
Direct calculation
Constructing mirror manifolds
Examples / 5.5.:
Implications / 5.6.:
Spacetime topology change
Basic ideas
Mild topology change
Kahler moduli space / 6.2.1.:
Complex structure moduli space / 6.2.3.:
Implications of mirror manifolds: revisited / 6.2.4.:
Flop transitions / 6.2.5.:
An example / 6.2.6.:
Drastic topology change
Strominger's resolution of the conifold singularity / 6.3.1.:
Conifold transitions and topology change / 6.3.3.:
Symmetry Approach to the XXZ Model / T. MiwaCourse 5.:
The XXZ Hamiltonian for [Delta] [ -1
Transfer matrix
Symmetry of U[subscript q](sl[subscript 2])
Corner transfer matrix
Level 1 highest weight module
Half transfer matrix
Intertwiners
The vacuum vector
Diagonalization of the transfer matrix
Local operators and difference equations
Superstring Dualities, Dirichlet Branes and the Small Scale Structure of Space / M.R. DouglasSeminar 1.:
Duality and solitons in supersymmetric field theory
Duality and solitons in superstring theory
Dirichlet branes
Short distances in superstring theory
Further directions
Testing the Standard Model and Beyond / J. EllisSeminar 2.:
Introduction to the Standard Model and its (non-topological) defects
Testing the Standard Model
The electroweak vacuum
Motivations for supersymmetry
Model building
Physics with the LHC
Quantum Group Approach to Strongly Coupled Two Dimensional Gravity / J.-L. GervaisSeminar 3.:
Basic points about Liouville theory
The basic relations between 6j symbols
The Liouville string
Concluding remarks
N = 2 Superalgebra and Non-Commutative Geometry / H. Grosse ; C. Klimcik ; P. PresnajderSeminar 4.:
Commutative supersphere
Non-commutative supersphere
Outlook
Lecture on N = 2 Supersymmetric Gauge Theory / W. LercheSeminar 5.:
Semi-classical N = 2 Yang-Mills theory for G = SU(2)
The exact quantum moduli space
Solving the monodromy problem
Picard-Fuchs equations
Generalization to SU(n)
Physics / Part II.:
Noncommutative Geometry: The Spectral Aspect / A. ConnesCourse 6.:
Noncommutative geometry: an introduction
Infinitesimal calculus
Local index formula and the transverse fundamental class
The notion of manifold and the axioms of geometry
The spectral geometry of space-time
The KZB Equations on Riemann Surfaces / G. FelderCourse 7.:
Conformal blocks on Riemann surfaces
Kac-Moody groups
Principal G-bundles
Conformal blocks
The connection
The energy-momentum tensor
Flat structures
Connections on bundles of projective spaces / 3.3.:
The Friedan-Shenker connection / 3.4.:
The Knizhnik-Zamolodchikov-Bernard equations
Dynamical r-matrices
An explicit form for the connection
Transformation properties
Moving points
Fixing the complex structure
Proof of Theorem 5.2
From Diffeomorphism Groups to Loop Spaces via Cyclic Homology / J.-L. LodayCourse 8.:
Diffeomorphism group and pseudo-isotopy space
Algebraic K-theory via Quillen +-construction
The +-construction
First definition of Waldhausen's space A(X)
The Grothendieck group K[subscript 0]
Hochschild and cyclic homology, Lie algebras
Hochschild homology
Cyclic homology
Relationship with the Lie algebra homology of matrices
Computing A(X) out of the loop space [Lambda]X
Algebraic K-theory via Waldhausen S.-construction and Wh(X)
Waldhausen S.-construction
A(X) and Wh(X) via the S.-construction
Relating Wh(X) to pseudo-isotopy
Notation and terminology in algebraic topology / Appendix A.:
Homotopy theory / A.1.:
Classifying spaces / A.2.:
Simplicial sets and classifying spaces / Appendix B.:
More on classifying spaces of categories / B.1.:
Bisimplicial sets / B.2.:
References with comments
Quantum Groups and Braid Groups / M. RossoCourse 9.:
The Yang-Baxter equation, braid groups and Hopf algebras
Drinfeld's quantum double
The dual double construction
The quantum double and its properties
Hopf pairings and a generalized double
The quantized enveloping algebra U[subscript q]G
Construction of U[subscript q]G
A Hopf pairing U[subscript +] [times] U[subscript -] [right arrow] C(q) / 4.1.1.:
Some results from representation theory
The quantum shuffle construction
The quantum shuffle Hopf algebra
Hopf bimodules
Braidings
The cotensor Hopf algebra
The quantum symmetric algebra
The examples from abelian group algebras
A classification result
Multiplicative bases in the quantum shuffle algebra / 5.3.1.:
Consequences of growth conditions / 5.3.2.:
From Index Theory to Non-Commutative Geometry / N. TelemanCourse 10.:
Differential forms on smooth and Lipschitz manifolds
Riemannian metrics and L[subscript 2]-forms on smooth and Lipschitz manifolds
Hodge theory on smooth and Lipschitz manifolds
Analytical index of Fredholm operators on smooth and Lipschitz manifolds
Topological K-theory
Symbols of elliptic operators on smooth manifolds and their index
Characteristic classes, Chern character
Stiefel-Whitney classes of real vector bundles
Chern classes of complex vector bundles
Pontrjagin classes of real vector bundles
Chern-Weyl theory on smooth manifolds
Thom isomorphism
Thom isomorphism in cohomology
Thom isomorphism in K-theory
Comparison between the Thom isomorphism in cohomology and K-theory
Index theorem for smooth manifolds
Index theorem for Lipschitz manifolds
Quasi local formulas for Thom-Hirzebruch classes on quasi conformal manifolds
Compact Quantum Groups / S.L. WoronowiczCourse 11.:
Definitions and results
The Haar measure
Unitary representations
Right regular representation
The Hopf algebras
Peter-Weyl theory
Groups with faithful Haar measure
Seiberg-Witten Invariants and Vortex Equations / O. Garcia-PradaSeminar 6.:
Preliminaries on spin geometry, almost-complex geometry and self-duality
The Seiberg-Witten invariants
Kahler complex surfaces
Non-Kahler complex surfaces
Symplectic four-manifolds
Non-Abelian monopole equations
Quantization of Poisson Algebraic Groups and Poisson Homogeneous Spaces / P. Eting of ; D. KazhdanSeminar 7.:
Quantization of Poisson algebraic and Lie groups
Quantization of Poisson homogeneous spaces
Eta and Torsion / J. LottSeminar 8.:
Eta-invariant
Analytic torsion
Eta-forms
Analytic torsion forms
Symplectic Formalism in Conformal Field Theory / A. SchwarzSeminar 9.:
Symplectic formalism in classical field theory
Superconformal geometry
Superconformal field theory
Quantization of geometry associated to the quantized Knizhnik-Zamolodchikov equations / A. VarchenkoSeminar 10.:
KZ equations
Hypergeometric functions
Geometry of hypergeometric functions
qKZ equations
Solutions to the qKZ equations and eigenvectors of commuting Hamiltonians
Solutions to the qKZ equations
Difference equations of the discrete connection
p-Homology theory
Conclusion
Lecturers
Seminar Speakers
Participants
6.

図書

図書
A.Yu. Morozov, M.A. Olshanetsky, editors
出版情報: Providence, R.I. : American Mathematical Society, c1999-  v. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 191, v. 221 . Advances in the mathematical sciences (formerly advances in Soviet mathematics) ; 43, 60
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Hecke-Tyurin parametrization of the Hitchin and KZB systems / B. Enriquez ; V. Rubtsov
Combinatorics and geometry of higher level Weyl modules / B. Feigin ; A. N. Kirillov ; S. Loktev
Cosh-Gordon equation and quasi-Fuchsian groups / V. V. Fock
On a class of representations of quantum groups and its applications / A. Gerasimov ; S. Kharchev ; D. Lebedev ; S. Oblezin
On syzygies of highest weight orbits / A. L. Gorodentsev ; A. S. Khoroshkin ; A. N. Rudakov
On finest and modular t-stabilities / S. A. Kuleshov
Hochschild homology and Gabber's theorem / D. Kaledin
Method of projections of Drinfeld currents / S. Khoroshkin ; S. Pakuliak
On rational and elliptic forms and Painleve VI equation / A. Levin ; A. Zotov
Determinantal point processes and fermionic Fock space / Y. A. Neretin
On adelic model of boson Fock space
Hypercomplex manifolds with trivial canonical bundle and their holonomy / M. Verbitsky
Hecke-Tyurin parametrization of the Hitchin and KZB systems / B. Enriquez ; V. Rubtsov
Combinatorics and geometry of higher level Weyl modules / B. Feigin ; A. N. Kirillov ; S. Loktev
Cosh-Gordon equation and quasi-Fuchsian groups / V. V. Fock
7.

図書

図書
editors Boris N. Apanasov ... [et al.]
出版情報: Berlin : Walter de Gruyter, 1997  xii, 348 p. ; 25 cm
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8.

図書

図書
edited by Alexander G. Ramm
出版情報: New York : Plenum Press, c1998  viii, 207 p. ; 26 cm
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9.

図書

図書
Masaki Kashiwara ... [et al.], editors
出版情報: Boston : Birkhäuser, c1998  vi, 493 p. ; 25 cm
シリーズ名: Progress in mathematics ; vol. 160
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10.

図書

図書
edited by A. Comtet, T. Jolicœur, S. Ouvry and F. David
出版情報: Berlin : Springer in cooperation with the NATO Scientific Affair Division , Les Ulis : EDP sciences, 1999  xxxiv, 909 p. ; 23 cm
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Lecturers
Participants
Préface
Preface
Contents
Electrons in a Flatland / M. ShayeganCourse 1:
Introduction / 1:
Samples and measurements / 2:
2D electrons at the GaAs/AlGaAs interface / 2.1:
Magnetotransport measurement techniques / 2.2:
Ground states of the 2D System in a strong magnetic field / 3:
Shubnikov-de Haas oscillations and the IQHE / 3.1:
FQHE and Wigner crystal / 3.2:
Composite fermions / 4:
Ferromagnetic state at ν = 1 and Skyrmions / 5:
Correlated bilayer electron states / 6:
Overview / 6.1:
Electron System in a wide, single, quantum well / 6.2:
Evolution of the QHE states in a wide quantum well / 6.3:
Evolution of insulating phases / 6.4:
Many-body, bilayer QHE at ν = 1 / 6.5:
Spontaneous interlayer Charge transfer / 6.6:
Summary / 6.7:
The Quantum Hall Effect: Novel Excitations and Broken Symmetries / S.M.GirvinCourse 2:
The quantum Hall effect
Why 2D is important / 1.1:
Constructing the 2DEG / 1.3:
Why is disorder and localization important? / 1.4:
Classical dynamics / 1.5:
Semi-classical approximation / 1.6:
Quantum dynamics in strong B Fields / 1.7:
IQHE edge states / 1.8:
Semiclassical percolation picture / 1.9:
Fractional QHE / 1.10:
The ν = 1 many-body state / 1.11:
Neutral collective excitations / 1.12:
Charged excitations / 1.13:
FQHE edge states / 1.14:
Quantum hall ferromagnets / 1.15:
Coulomb exchange / 1.16:
Spin wave excitations / 1.17:
Effective action / 1.18:
Topological excitations / 1.19:
Skyrmion dynamics / 1.20:
Skyrme lattices / 1.21:
Double-layer quantum Hall ferromagnets / 1.22:
Pseudospin analogy / 1.23:
Experimental background / 1.24:
Interlayer phase coherence / 1.25:
Interlayer tunneling and tilted field effects / 1.26:
Lowest Landau level projection / Appendix A:
Berry's phase and adiabatic transport / Appendix B:
Aspects of Chern-Simons Theory / G.V.DunneCourse 3:
Basics of planar field theory
Chern-Simons coupled to matter fields - "anyons"
Maxwell-Chern-Simons: Topologically massive gauge theory
Fermions in 2 + 1-dimensions / 2.3:
Discrete symmetries: <$>{\cal P}, {\cal C}<$> and <$>{\cal T}<$> / 2.4:
Poincaré algebra in 2 + 1-dimensions / 2.5:
Nonabelian Chern-Simons theories / 2.6:
Canonical quantization of Chern-Simons theories
Canonical structure of Chern-Simons theories
Chern-Simons quantum mechanics
Canonical quantization of abelian Chern-Simons theories / 3.3:
Quantization on the torus and magnetic translations / 3.4:
Canonical quantization of nonabelian Chern-Simons theories / 3.5:
Chern-Simons theories with boundary / 3.6:
Chern-Simons vortices
Abelian-Higgs model and Abrikosov-Nielsen-Olesen vortices / 4.1:
Relativistic Chern-Simons vortices / 4.2:
NonabelianrelativisticChern-Simonsvortices / 4.3:
Nonrelativistic Chern-Simons vortices: Jackiw-Pi model / 4.4:
NonabeliannonrelativisticChern-Simonsvortices / 4.5:
Vortices in the Zhang-Hansson-Kivelson model for FQHE / 4.6:
Vortex dynamics / 4.7:
Induced Chern-Simons terms
Perturbatively induced Chern-Simons terms: Fermion loop / 5.1:
Induced currents and Chern-Simons terms / 5.2:
Induced Chern-Simons terms without fermions / 5.3:
A finite temperature puzzle / 5.4:
Quantum mechanical finite temperature model / 5.5:
Exact finite temperature 2 + 1 effective actions / 5.6:
Finite temperature perturbation theory and Chern-Simons terms / 5.7:
Anyons / J. MyrheimCourse 4:
The concept of particle statistics
Statistical mechanics and the many-body problem
Experimental physics in two dimensions
The algebraic approach: Heisenberg quantization
More general quantizations
The configuration space
The Euclidean relative space for two particles
Dimensions d = 1, 2, 3
Homotopy
The braid group
Schrödinger quantization in one dimension
Heisenberg quantization in one dimension
The coordinate representation
Schrödinger quantization in dimension d ≥ 2
Scalar wave functions
Interchange phases
The statistics vector potential
The N-particle case
Chern-Simons theory
The Feynman path integral for anyons
Eigenstates for Position and momentum
The path integral
Conjugation classes in SN
The non-interacting case
Duality of Feynman and Schrödinger quantization
The harmonic oscillator / 7:
The two-dimensional harmonic oscillator / 7.1:
Two anyons in a harmonic oscillator potential / 7.2:
More than two anyons / 7.3:
The three-anyon problem / 7.4:
The anyon gas / 8:
The cluster and virial expansions / 8.1:
First and second order perturbative results / 8.2:
Regularization by periodic boundary conditions / 8.3:
Regularization by a harmonic oscillator potential / 8.4:
Bosons and fermions / 8.5:
Two anyons / 8.6:
Three anyons / 8.7:
The Monte Carlo method / 8.8:
The path integral representation of the coefficients <$>G_{\cal P}<$> / 8.9:
Exact and approximate polynomials / 8.10:
The fourth virial coefficient of anyons / 8.11:
Two polynomial theorems / 8.12:
Charged particles in a constant magnetic field / 9:
One particle in a magnetic field / 9.1:
Two anyons in a magnetic field / 9.2:
The anyon gas in a magnetic field / 9.3:
Interchange phases and geometric phases / 10:
Introduction to geometric phases / 10.1:
Two particles in a magnetic field / 10.2:
Interchange of two anyons in potential wells / 10.4:
Laughlin's theory of the fractional quantum Hall effect / 10.5:
Generalized Statistics in One Dimension / A.P. PolychronakosCourse 5:
Permutation group approach
Realization of the reduced Hilbert space
Path integral and generalized statistics
Cluster decomposition and factorizability
One-dimensional systems: Calogero model
The Calogero-Sutherland-Moser model
Large-N properties of the CSM model and duality
One-dimensional systems: Matrix model
Hermitian matrix model
The unitary matrix model
Quantization and spectrum
Reduction to spin-particle systems
Operator approaches
Exchange operator formalism
Systems with internal degrees of freedom
Asymptotic Bethe ansatz approach
The freezing trick and spin models
Exclusion statistics
Motivation from the CSM model
Semiclassics - Heuristics
Exclusion statistical mechanics
Exclusion statistics path integral
Is this the only "exclusion" statistics?
Epilogue
Lectures on Non-perturbative Field Theory and Quantum Impurity Problems / H.SaleurCourse 6:
Some notions of conformal field theory
The free boson via path integrals
Normal ordering and OPE
The stress energy tensor
Conformal in(co)variance
Some remarks on Ward identities in QFT
The Virasoro algebra: Intuitive introduction
Cylinders
The free boson via Hamiltonians
Modular invariance
Conformal invariance analysis of quantum impurity fixed points
Boundary conformal field theory
Partition functions and boundary states
Boundary entropy
The boundary sine-Gordon model: General results
The model and the flow
Perturbation near the UV fixed point
Perturbation near the IR fixed point
An alternative to the instanton expansion: The conformal invariance analysis
Search for integrability: Classical analysis
Quantum integrability
Conformal perturbation theory
S-matrices
Back to the boundary sine-Gordon model
The thermodynamic Bethe-ansatz: The gas of particles with "Yang-Baxter statistics"
Zamolodchikov Fateev algebra
The TBA
A Standard computation: The central Charge
Thermodynamics of the flow between N and D fixed points
Using the TBA to compute static transport properties
Tunneling in the FQHE
Conductance without impurity
Conductance with impurity
Quantum Partition Noise and the Detection of Fractionally Charged Laughlin Quasiparticles / D.C. GlattliSeminar 1:
Partition noise in quantum conductors
Quantum partition noise
Partition noise and quantum statistics
Quantum conductors reach the partition noise limit
Experimental evidences of quantum partition noise in quantum conductors
Partition noise in the quantum Hall regime and determination of the fractional Charge
Edge states in the integer quantum Hall effect regime
Tunneling between IQHE edge channels and partition noise
Edge channels in the fractional regime
Noise predictions in the fractional regime
Measurement of the fractional Charge using noise
Beyond the Poissonian noise of fractional charges
Mott Insulators, Spin Liquids and Quantum Disordered Superconductivity / Matthew P.A. FisherCourse 7:
Models and metals
Noninteracting electrons
Interaction effects
Mott insulators and quantum magnetism
Spin models and quantum magnetism
Spin liquids
Bosonization primer
2 Leg Hubbard ladder
Bonding and antibonding bands
Interactions
Bosonization
d-Mott phase
Symmetry and doping
d-Wave superconductivity
BGS theory re-visited
d-wave symmetry
Continuum description of gapless quasiparticles
Effective field theory
Quasiparticles and phase flucutations
Nodons
Vortices
ic/2e versus hc/e vortices
Duality
Nodal liquid phase
Half-filling
Doping the nodal liquid
Closing remarks
Lattice duality
Two dimensions / A.1:
Three dimensions / A.2:
Statistics of Knots and Entangled Random Walks / S. NechaevCourse 8:
Lecturers
Participants
Préface
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