Integrable Quantum Field Theories 1102-4IQFT
The aim of the lectures is to introduce students to the formalism of Integrable Quantum Field Theories (IQFT). IQFT’s are a special type of quantum field theories which are exactly solvable. For example, the exact scattering matrix (S-matrix) is known for such theories. IQFT’s find applications in various places of modern physics. The list includes:
- applications in condensed matter to describe strongly correlated, low dimensional systems,
- in high-energy physics in studies of supersymmetric gauge theories (like N=4 super Yang-Mills theory),
- in mathematical physics due to intricate relations to quantum groups.
- IQFT’s are also intimately connected to Conformal Field Theories.
Beside these deep relations with many advanced aspects of physics, IQFT’s are also a fun place to learn more about the QFT’s in general. In an IQFT we can compute many quantities exactly without relying on the perturbation theory. This gives us direct access to non-perturbative physics and allows to illustrate technically involved concepts like solitons, kinks, bounds states and correlation functions with a relative ease. All irrespective of interaction’s strength.
The plan of the lectures:
1. QFT in 1+1 dimensions and integrability of the Sinh-Gordon theory
2. Spectrum, exact S-matrices, and Sine-Gordon theory
3. Basics of Conformal Field Theories (CFT); from CFT to IQFT
4. Thermodynamics and hydrodynamics of integrable theories
Main fields of studies for MISMaP
Type of course
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
Students understand basic features of integrable quantum field theories and the role of the S-matrix. Know examples of integrable QFT’s, are familiar with the Fadeev-Zamolodchikov algebra and the construction of the Thermodynamic Bethe Ansatz. Student knows applications of IQFT’s in modern physics. Student is able to solve basic problems in the field.
Assessment criteria
The final grade will consist of equally weighted 3 ingredients
- homeworks
- small research project
- final written exam
Small research projects are presented by students at the end of the semester. Students will choose a topic, according to their interests, in the middle of the semester. The topics will either explore more foundations of the IQFT’s or be directed at one of the modern applications.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: