Title Page

Title Page

Indice

Indice

Foreword

Foreword

Gruppo fotografico dei partecipanti al Corso

Gruppo fotografico dei partecipanti al Corso

Principles of chiral perturbation theory

Principles of chiral perturbation theory

Introduction

Introduction

Goldstone theorem

Goldstone theorem

QCD

QCD

Massless quarks

Massless quarks

Spontaneous breakdown of chiral symmetry

Spontaneous breakdown of chiral symmetry

Quark masses

Quark masses

Approximate chiral symmetry

Approximate chiral symmetry

Pion pole dominance

Pion pole dominance

Strength of the effective interaction

Strength of the effective interaction

Effective Lagrangian

Effective Lagrangian

Symmetries of the effective theory

Symmetries of the effective theory

Transformation law of the pion field

Transformation law of the pion field

Form of the effective Lagrangian

Form of the effective Lagrangian

Geometry and universality

Geometry and universality

Symmetry breaking

Symmetry breaking

Mass of the Goldstone bosons

Mass of the Goldstone bosons

Currents and external fields

Currents and external fields

Multipion exchange, unitarity and loops

Multipion exchange, unitarity and loops

Ward identities

Ward identities

Anomalies

Anomalies

Higher orders in L_(eff)

Higher orders in L_(eff)

Renormalizability

Renormalizability

Illustration: electromagnetic form factor

Illustration: electromagnetic form factor

Magnitude of the coupling constants

Magnitude of the coupling constants

Lattice-regularized QCD at finite temperature

Lattice-regularized QCD at finite temperature

Introduction

Introduction

Equation of state for SU(N) gauge theories

Equation of state for SU(N) gauge theories

Screening masses and perturbation theory

Screening masses and perturbation theory

Cut-off dependence of thermodynamics

Cut-off dependence of thermodynamics

Extrapolation to the continuum limit

Extrapolation to the continuum limit

QCD with light quarks

QCD with light quarks

The chiral phase transition

The chiral phase transition

The chiral transition in two-flavour QCD

The chiral transition in two-flavour QCD

Hadronic properties close to T_c

Hadronic properties close to T_c

The GMOR relation and the pion decay constant

The GMOR relation and the pion decay constant

Vector-meson mass and nucleon mass

Vector-meson mass and nucleon mass

Conclusions

Conclusions

Thermalization and colour deconfinement in high-energy nuclear collisions

Thermalization and colour deconfinement in high-energy nuclear collisions

Introduction

Introduction

Thermalization

Thermalization

Hadrosynthesis

Hadrosynthesis

The resonance gas

The resonance gas

Thermalization patterns

Thermalization patterns

Colour deconfinement

Colour deconfinement

Hard probes

Hard probes

Quarkonium production in hadron-hadron collisions

Quarkonium production in hadron-hadron collisions

Quarkonium production in a confined medium

Quarkonium production in a confined medium

Quarkonium production as deconfinement probe

Quarkonium production as deconfinement probe

The analysis of charm onium suppression

The analysis of charm onium suppression

Quarkonium interactions in QCD

Quarkonium interactions in QCD

Introduction

Introduction

Preview

Preview

QCD atoms in external fields

QCD atoms in external fields

Operator product expansion for quarkonium interactions

Operator product expansion for quarkonium interactions

General idea

General idea

Wilson coefficients

Wilson coefficients

Sum rules

Sum rules

Absorption cross-sections

Absorption cross-sections

Scale anomaly, chiral symmetry and low-energy theorems

Scale anomaly, chiral symmetry and low-energy theorems

Scale anomaly and quarkonium interactions

Scale anomaly and quarkonium interactions

Low-energy theorem for quarkonium interactions with pions

Low-energy theorem for quarkonium interactions with pions

The phase of the scattering amplitude

The phase of the scattering amplitude

Quarkonium interactions in matter

Quarkonium interactions in matter

Nuclear matter

Nuclear matter

Hadron gas

Hadron gas

Deconfined matter

Deconfined matter

Discussion and outlook

Discussion and outlook

Nonperturbative effects in heavy-flavour decays

Nonperturbative effects in heavy-flavour decays

Introduction

Introduction

Operator product expansion

Operator product expansion

Polarization operator and e^+ e^- annihilation into hadrons

Polarization operator and e^+ e^- annihilation into hadrons

Higher orders and infrared renormalons

Higher orders and infrared renormalons

Factorization of short and large distances and OPE

Factorization of short and large distances and OPE

OPE for heavy flavours. Total semileptonic widths

OPE for heavy flavours. Total semileptonic widths

Motion of the heavy quark

Motion of the heavy quark

Kinematics

Kinematics

Construction of OPE. Scaling

Construction of OPE. Scaling

Universal distribution function

Universal distribution function

Conclusions

Conclusions

Mechanisms for colour confinement

Mechanisms for colour confinement

Introduction

Introduction

Lattice QCD

Lattice QCD

Confinement of colour

Confinement of colour

Basic superconductivity

Basic superconductivity

Monopoles

Monopoles

Generalities on monopoles

Generalities on monopoles

't Hooft-Polyakov monopoles

't Hooft-Polyakov monopoles

The Abelian projection in QCD

The Abelian projection in QCD

Monopoles and confinement in QCD

Monopoles and confinement in QCD

Detecting dual superconductivity

Detecting dual superconductivity

U(1) gauge group

U(1) gauge group

Monopole condensation in SU(2), SU(3) gauge theories

Monopole condensation in SU(2), SU(3) gauge theories

Outlook and future perspectives

Outlook and future perspectives

Dual Abrikosov vortices in U(1) and SU(2) lattice gauge theories

Dual Abrikosov vortices in U(1) and SU(2) lattice gauge theories

Introduction

Introduction

Abrikosov vortices

Abrikosov vortices

London theory

London theory

Lattice Higgs in the London limit

Lattice Higgs in the London limit

Dual superconductivity in pure U(1) gauge theory

Dual superconductivity in pure U(1) gauge theory

Duality transformations in U(1)

Duality transformations in U(1)

Generalization to pure SU(2) and SU(3) gauge theories

Generalization to pure SU(2) and SU(3) gauge theories

External electric field

External electric field

Appendix A - Notation conventions

Appendix A - Notation conventions

Lattice differential forms

Lattice differential forms

Euclidean Maxwell equations

Euclidean Maxwell equations

Confinement and renormalization

Confinement and renormalization

Introduction

Introduction

Effective theory of confinement

Effective theory of confinement

Centre symmetry

Centre symmetry

Functional Schrodinger representation

Functional Schrodinger representation

Dimensional vs. lattice regularization

Dimensional vs. lattice regularization

Singular configurations

Singular configurations

Effective theory

Effective theory

Sine-Gordon model

Sine-Gordon model

Haaron gas

Haaron gas

Static charges

Static charges

Nambu--Jona-Lasinio model

Nambu--Jona-Lasinio model

Haaron gas and localization

Haaron gas and localization

Double role of V(u)

Double role of V(u)

Centre symmetry and instantons

Centre symmetry and instantons

Universality and condensates

Universality and condensates

Localized saddle points

Localized saddle points

Bare vs. renormalized expansion

Bare vs. renormalized expansion

Mini-instantons

Mini-instantons

Multiple fixed points

Multiple fixed points

Theory of everything

Theory of everything

From the superconductor to the standard model

From the superconductor to the standard model

Wegner-Haughton equation

Wegner-Haughton equation

I.r. fixed point

I.r. fixed point

Couplings of the Goldstone modes

Couplings of the Goldstone modes

Conclusions

Conclusions

Dynamics of the colour flux tube in lattice gauge systems

Dynamics of the colour flux tube in lattice gauge systems

Introduction

Introduction

Special features of the 3D Z_2 gauge model

Special features of the 3D Z_2 gauge model

Vibrations of the colour flux tube

Vibrations of the colour flux tube

Width of the colour flux tube

Width of the colour flux tube

Results of Z_2 gauge model

Results of Z_2 gauge model

Interacting flux tubes

Interacting flux tubes

Thermal phase transition in QCD

Thermal phase transition in QCD

Introduction

Introduction

Pure Yang-Mills theory: deconfinement phase transition

Pure Yang-Mills theory: deconfinement phase transition

Bubble confusion

Bubble confusion

QCD with massless quarks

QCD with massless quarks

Properties of the phase transition. The real world

Properties of the phase transition. The real world

Instantons and percolation

Instantons and percolation

Disoriented chiral condensate

Disoriented chiral condensate

Applications of the model of the stochastic vacuum

Applications of the model of the stochastic vacuum

Introduction

Introduction

Notation

Notation

The nonperturbative QCD vacuum

The nonperturbative QCD vacuum

Renormalons

Renormalons

The nonperturbative operator product expansion

The nonperturbative operator product expansion

The nonperturbative background field and nonlocal condensates

The nonperturbative background field and nonlocal condensates

The model of the stochastic vacuum

The model of the stochastic vacuum

Relation to functional integrals

Relation to functional integrals

Cluster expansion for commuting stochastic variables

Cluster expansion for commuting stochastic variables

Abelian model. Confinement in the presence of monopoles

Abelian model. Confinement in the presence of monopoles

Non-Abelian model

Non-Abelian model

The Gaussian model

The Gaussian model

Applications

Applications

Static potentials

Static potentials

String formation

String formation

Soft high-energy scattering

Soft high-energy scattering

Hot nonperturbative QCD

Hot nonperturbative QCD

Introduction

Introduction

New background field formalism

New background field formalism

The temperature phase transition in QCD

The temperature phase transition in QCD

Spatial Wilson loops

Spatial Wilson loops

Screening masses of mesons and glueballs

Screening masses of mesons and glueballs

Infrared catastrophe in hot QCD

Infrared catastrophe in hot QCD

Conclusions

Conclusions

Dyons in QCD: confinement and chiral-symmetry breaking

Dyons in QCD: confinement and chiral-symmetry breaking

Introduction

Introduction

Properties of dyonic solutions

Properties of dyonic solutions

Dyonic gas

Dyonic gas

Confinement due to dyons

Confinement due to dyons

Chiral-symmetry breaking in the dyonic gas

Chiral-symmetry breaking in the dyonic gas

Conclusions and prospectives

Conclusions and prospectives

Tunneling phenomena in QCD and hadronic structure

Tunneling phenomena in QCD and hadronic structure

Introduction

Introduction

Correlation functions of the QCD vacuum

Correlation functions of the QCD vacuum

Hadronic structure and the vacuum

Hadronic structure and the vacuum

Why the correlation functions?

Why the correlation functions?

Classification of correlation functions

Classification of correlation functions

Phenomenology of me sonic correlation functions

Phenomenology of me sonic correlation functions

Tunneling phenomena and instantons

Tunneling phenomena and instantons

Brief introduction to instantons

Brief introduction to instantons

Instantons and anomalous fermion production

Instantons and anomalous fermion production

The <> model

The <> model

Interacting instantons

Interacting instantons

Glueballs and instantons

Glueballs and instantons

Correlation functions at finite temperature

Correlation functions at finite temperature

The phase transition

The phase transition

Instantons at finite temperatures

Instantons at finite temperatures

Summary

Summary

Chiral-symmetry breaking by instantons

Chiral-symmetry breaking by instantons

Foreword

Foreword

Periodicity of the Yang-Mills potential energy

Periodicity of the Yang-Mills potential energy

Instanton configurations

Instanton configurations

Gluon condensate

Gluon condensate

One-instanton weight

One-instanton weight

Instanton ensemble

Instanton ensemble

Chiral-symmetry breaking in QCD

Chiral-symmetry breaking in QCD

Chiral-symmetry breaking by definition

Chiral-symmetry breaking by definition

Chiral-symmetry breaking by instantons: qualitative derivation

Chiral-symmetry breaking by instantons: qualitative derivation

Derivation II: quark propagator

Derivation II: quark propagator

Derivation III: Nambu--Jona-Lasinio model

Derivation III: Nambu--Jona-Lasinio model

N_f = 1

N_f = 1

N_f = 2

N_f = 2

Any N_f

Any N_f

QCD at still lower energies

QCD at still lower energies

How instantons may help confinement

How instantons may help confinement

Topological properties of QCD and lattice approach

Topological properties of QCD and lattice approach

Introduction

Introduction

A large-N explanation of the U(1)_A problem

A large-N explanation of the U(1)_A problem

QCD on the lattice

QCD on the lattice

The topological susceptibility on the lattice

The topological susceptibility on the lattice

A determination of Chi by a field-theoretical method

A determination of Chi by a field-theoretical method

CP^(N-1) models

CP^(N-1) models

Spin content of the proton

Spin content of the proton

Recent results in high-temperature lattice gauge theories

Recent results in high-temperature lattice gauge theories

Introduction

Introduction

Finite-temperature LGT

Finite-temperature LGT

General setting

General setting

Svetitsky-Yaffe conjecture

Svetitsky-Yaffe conjecture

The SU(2) case: character expansion

The SU(2) case: character expansion

Construction of the effective action

Construction of the effective action

Expansion in beta_s of the effective action

Expansion in beta_s of the effective action

Zeroth-order approximation

Zeroth-order approximation

First-order approximation

First-order approximation

The adjoint-representation term

The adjoint-representation term

Pair of fundamental representations

Pair of fundamental representations

Independent approach to N_t = 1

Independent approach to N_t = 1

Determination of T_c

Determination of T_c

Conclusions

Conclusions

Appendix

Appendix

QCD sum rules and predictions in the charmonium spectrum

QCD sum rules and predictions in the charmonium spectrum

Introduction

Introduction

Foundations and basic formulae

Foundations and basic formulae

2.1.

2.1.

2.2.

2.2.

2.3.

2.3.

Fixing parameters in the 3S_1 channel of charmonium

Fixing parameters in the 3S_1 channel of charmonium

3.1.

3.1.

3.2.

3.2.

3.3.

3.3.

Predictions in the 1S_0 and 1P_1 channels

Predictions in the 1S_0 and 1P_1 channels

4.1.

4.1.

4.2.

4.2.

Final remarks

Final remarks

Quarks, mesons and (Exact) flow equations

Quarks, mesons and (Exact) flow equations

Chiral-symmetry breaking in QCD

Chiral-symmetry breaking in QCD

A qualitative picture

A qualitative picture

An exact renormalization group equation

An exact renormalization group equation

The chiral anomaly and the O(4) model

The chiral anomaly and the O(4) model

Results

Results

Conclusions

Conclusions

Elenco dei partecipanti

Elenco dei partecipanti