格子規範理論簡介(一)：標量與純規範理論
Introduction to Lattice Gauge Theory (I): Scalar and Pure Gauge Theory
| 節 | 週四 |
|---|---|
3 10:10–11:00 | 格子規範理論簡介(一)：標量與純規範理論 SC157 2 節連堂 |
4 11:10–12:00 |
* 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. In this course we will learn the formalism to address the physics of systems that interact via the exchange of gauge bosons. These are called Yang-Mills theories and we will discuss them both with Abelian and non-Abelian gauge groups. Expanding our findings to theories that also include scalar particles we will study the physics of the Higgs boson in the Standard Model. By pushing even further and adding in fermions we will finally arrive at a fully non-perturbative description of quantum chromodynamics, the theory of the strong force. Our research will lead us to the realisation that a full result requires the numerical simulation of the system on a (super-)computer and we will practice how to perform such simulations. In addition we will learn how to derive meaningful physics results that cannot be obtained any other way. Throughout emphasis is put on practical implementations. This course is the first part of a two-part series. Wanting to perform numerical calculations access to a laptop with internet connection is required as well as some interest in writing Python programs. During the course we will develop codes for: - The bootstrap resampling and fitting of data with a linear ansatz - The simulation of the Ising Model using a Heatbath algorithm - The simulation of scalar field theory using the Hybrid Monte Carlo algorithm - Inversion of a fermion matrix using the Conjugate Gradient algorithm In contract to the previous course of the same name the material is organised slightly differently: This time we will already encounter quarks and how to include them systematically already in this course.
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 | Introduction and discussion of course format |
| 第 2 週 | Primer on quantum mechanics and quantum field theory |
| 第 3 週 | Primer on statistical mechanics and spin systems |
| 第 4 週 | Numerical methods: Markov chain Monte-Carlo |
| 第 5 週 | Numerical methods: Importance sampling and Metropolis algorithm in spin systems |
| 第 6 週 | Basics of data science: Resampling and chi^2 fitting |
| 第 7 週 | Scalar field theory in the continuum |
| 第 8 週 | Scalar field theory on the lattice |
| 第 9 週 | Primer on gauge theories in the continuum |
| 第 10 週 | (Non-)Abelian gauge theory on the lattice: Weak and strong coupling expansion |
| 第 11 週 | Non-Abelian gauge theory on the lattice: Confinement |
| 第 12 週 | Gauge-Higgs models |
| 第 13 週 | Theories with quarks and the problem with them |
| 第 14 週 | Fermions on the lattice |
| 第 15 週 | Numerical methods for fermions |
| 第 16 週 | Hadron spectroscopy |
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