by G. Mussardo (8 credits, type A)
Main Topics
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
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