The Graduate School in Physics of Torino University organizes different Ph.D. Programmes in Theoretical Physics that are related to the research lines pursued within the Department of Theoretical Physics and the INFN Sezione di Torino and are linked to international collaborations both at the scientific and teaching level.

The interested students are assumed to have preliminarily attended (or are invited to attend) courses equivalent to the following ones, given at Torino University:

• Meccanica Statistica
• Teorie Quantistiche

The curriculum in Statistical Field Theory is based on the following COURSES

1. Two dimensional Conformal Field Theories and Applications

Lecturer: M. Caselle
2. Constrained systems and BRST quantization of gauge theories

Lecturer: A. D'Adda
3. Introduction to statistical field theory: beta-functions and renormalization group

Lecturer: F. Gliozzi

The aim of the course is to give an introduction to 2d conformal field theories and to discuss their applications to the physics of 2d statistical models.

1. Conformal Field Theories and Statistical Mechanics.
• Scale invariance and critical points.
• Scaling and universality.
• Correlation functions and critical indices.
2. Introduction to the conformal group.
• Conformal group in d dimensions: constraints on the correlators.
• The d=2 case.
• Radial quantization and OPE.
• Conformal Ward identities.
• Virasoro algebra.
3. Conformal families.
• The Hilbert space of states.
• Primary and secondary fields
4. Bootstrap program and minimal models.
• Bootstrap and crossing symmetry.
• Null vectors.
• Minimal Models.
• Fusion Rules.
5. Example: the 2d Ising model.

The course is a short, elementary introduction to BRS symmetry and its geometrical meaning with some applications. The plan of the course is the following:

1. Introduction to gauge fixing and BRS symmetry.
2. The simplest possible example: abelian gauge symmetry in zero space-time dimensions.
3. Non abelian gauge group in zero dimensions and the geometric interpretation of the ghost-antighost system.
4. One dimensional example: quantization of a pointlike particle.
5. Quantization of string theory with BRS: derivation of the physical states and critical dimensions
6. A brief introduction to BRS symmetry in Yang-Mills theory (does not include quantization).

This introductory course to statistical field theory deals with the Wilson approach to the renormalization group applied to the critical phenomena and to relativistic quantum field theory. The plan of the course is the following

1. Introduction to critical phenomena
2. Ising model
3. Mean field approximation
4. Wilson renormalization group
5. Critical exponents
6. Beta function
7. Asymptotic freedom
8. Applications to two-dimensional models
9. Lattice Gauge theories.