格子規範理論簡介(二):費米子
Introduction to Lattice Gauge Theory (II): Fermions
| 節 | 週三 |
|---|---|
6 14:20–15:10 | 格子規範理論簡介(二):費米子 SC157 2 節連堂 |
7 15:30–16:20 |
* 根據陽明交大上課時間表所列
Lattice gauge theory (LGT) represents one of the most powerful and advanced formalisms in science to study the most fundamental dynamics of atomic and sub-atomic systems. It has applications that range from condensed matter to particle theory, from the study of phase transitions to quantum scattering. Some of the most important systems today are those that contain fermions as degrees of freedom. In this course we will learn the formalism to address systems with fermions and in particular gauge theories, such as quantum electrodynamics and quantum chromodynamics. These are the fundamental theories of electrons and quarks, respectively. From this we will see that a full result requires the numerical simulation of the system on a (super) computer. With this insight we will practice how to perform calculations on the computer and derive meaningful physics results that cannot be obtained any other way. Throughout emphasis is put on practical implementations. This course is the second part of a two-part series. However, the main findings of the first part will be reviewed. For this reason no prior knowledge of lattice gauge theory is required to participate in this course. Wanting to perform numerical calculations access to a laptop is required as well as some interest in writing Python programs.
Basic Python programming, Quantum mechanics Quantum field theory (optional) Statistical Physics (optional)
In this course we will actively develop Python programs to calculate some observables in Lattice Gauge Theory. Students will be asked to submit their developed programs through the year as homework projects.
100% homework projects.
| 週次 | 主題 |
|---|---|
| 第 1 週 | Motivation and introduction: Quarks and gluons, what are they? |
| 第 2 週 | Introduction to pure gauge theory: The theory of gluons. |
| 第 3 週 | Pure gauge theory on a lattice. |
| 第 4 週 | The gauge average and physic observables. |
| 第 5 週 | Numerical methods for pure gauge theories. |
| 第 6 週 | Theories with quarks and the problem with them. |
| 第 7 週 | Solution 1: Wilson Fermions. |
| 第 8 週 | Solution 2: Staggered Fermions. |
| 第 9 週 | Solution 3: Domain Wall Fermions and chiral symmetry on a lattice. |
| 第 10 週 | Numerical methods for theories with fermions. |
| 第 11 週 | Hadrons. The multi-quark states that make all matter. |
| 第 12 週 | (Optional) Scales and renormalization. |
| 第 13 週 | Introduction to high-performance computing. |
| 第 14 週 | Computing paradigms and code optimization as well as benchmarking. |
| 第 15 週 | Supercomputing architectures. CPU and GPU clusters. High-throughput computing. |
| 第 16 週 | Limits of current numerical methods. Alternative approach through AI or quantum computing? |
Gattringer, Lang, "Quantum Chromodynamics on the Lattice: An Introductory Presentation" (2009) Lehner/gpt: "A Python toolkit for lattice field theory" (https://github.com/lehner/gpt)
- 地點
- SC456
- 時間
- T10
- 聯絡方式
- afrancis@nycu.edu.tw