Quantum Fields on a Lattice II: Advanced Applications
This course covers quantum field theory on a lattice, with a focus on applications in a wide range of problems in quantum technology, quantum biophysics, and social dynamics.
Lecturer
Aleksandr Molochkov
Date
17th September, 2026 ~ 14th January, 2027
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 10:40 - 12:15 | Shuimo | - | - | - |
| Thursday | 13:30 - 15:05 | Shuimo | - | - | - |
Prerequisite
Basic knowledge of quantum mechanics and quantum field theory
Syllabus
The major themes of the course include the following:
1. Introduction to Quantum Field Theory: This section introduces the quantization of fields through the path integral approach and explores the connection between quantum field theory and statistical physics.
2. Lattice Discretization of Quantum Field Theory: Building on Wilson’s universality principle, we will investigate the discretization of space-time and the calculation of the path integral on a lattice. We will formulate the actions of scalar and gauge field theories within this discrete framework and analyze methods to compute key observable quantities from these theories.
3. Modern Techniques in Lattice Simulations and Data Analysis: In this part of the course, we review contemporary methods for lattice simulations and data analysis, highlighting the use of machine learning and quantum computers in these processes.
4. Applications of Lattice Quantum Field Theory: In the fourth section, we explore the modeling of various strongly correlated systems using lattice field theory. Specific topics will include effects observed in superfluids and superconductors, low-dimensional quantum systems, anomalous boundary effects, and the Casimir effect. We also discuss examples of protein structure and dynamics modeling within the Abelian Higgs Model. In the final part of the Applications section, we discuss the analysis of critical phenomena in social dynamics within statistical field theory models on the lattice.
1. Introduction to Quantum Field Theory: This section introduces the quantization of fields through the path integral approach and explores the connection between quantum field theory and statistical physics.
2. Lattice Discretization of Quantum Field Theory: Building on Wilson’s universality principle, we will investigate the discretization of space-time and the calculation of the path integral on a lattice. We will formulate the actions of scalar and gauge field theories within this discrete framework and analyze methods to compute key observable quantities from these theories.
3. Modern Techniques in Lattice Simulations and Data Analysis: In this part of the course, we review contemporary methods for lattice simulations and data analysis, highlighting the use of machine learning and quantum computers in these processes.
4. Applications of Lattice Quantum Field Theory: In the fourth section, we explore the modeling of various strongly correlated systems using lattice field theory. Specific topics will include effects observed in superfluids and superconductors, low-dimensional quantum systems, anomalous boundary effects, and the Casimir effect. We also discuss examples of protein structure and dynamics modeling within the Abelian Higgs Model. In the final part of the Applications section, we discuss the analysis of critical phenomena in social dynamics within statistical field theory models on the lattice.
Audience
Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English