### by G. Mussardo (8 credits)

*Main Topics*

Statistical Mechanics

- Basic postulates
- Ensembles
- Density matrix
- Indistinguishable particles
- Bose-Einstein and Fermi-Dirac statistics
- Chandrashekar limit
- Anyons

Phase transitions

- Symmetry and order parameters
- Critical exponents and scaling laws
- Lattice models and continuum limit

Bi-dimensional lattice models

- Duality of the Ising model
- Combinatorial solutions
- Transfer matrix and Yang-Baxter equations
- Bethe Ansatz
- Potts model, random walks and self-avoiding walks

Field Theory Approach to Critical Phenomena

- Feynman rules
- Wick theorem
- S-matrix
- Unitarity and crossing equations
- N-particle phase space, asymptotic and threshold behavior
- Euclidean Quantum Field Theories
- Path integral

Renormalization Group

- Effective Hamiltonians
- Running coupling constants and beta functions
- Fixed points and scaling region
- Relevant, irrelevant and marginal operators

Fermionic formulation of the 2-dimensional Ising model

- Order and disorder operators
- Operator product expansion and fermionic fields
- Dirac equation

Conformal Field Theory

- Conformal Invariance
- Ward identity and primary fields
- Virasoro algebra and central charge
- Representation theory
- Casimir effect and other finite size phenomena
- Bosonic and fermionic fields

Minimal models

- Differential equations of the correlation functions
- Gas di Coulomb
- Modular invariance
- Statistical Models with Supersymmetry
- Parafermionic and Wess-Zumino-Witten models