PHYS549 GEOMETRY OF GAUGE FIELDS
| Course Code: | 2300549 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Physics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. SEÇKİN KÜRKCÜOĞLU |
| Offered Semester: | Once in several years. |
Course Objectives
The aim of this course is to provide students with a rigorous understanding of the geometric framework underlying gauge theories. Through the study of principal bundles, connections, and curvature, students will learn how gauge-invariant field equations arise from variational principles, culminating in applications to Yang–Mills theory, Dirac fields, and the unification of gauge fields with gravitation.
Course Content
Principal fibber bundles and connections. Curvature and G-valued differential forms. Particle fields and gauge invariant Lagrangians. Principle of least action and Yang-Mills field equations. Free Dirac electron fields. Interactions. Orthonormal frame bundle. Linear connections and Riemannian curvature. Unification of gauge fields and gravitation.
Course Learning Outcomes
By the end of this course, students will be able to formulate gauge theories using the language of principal bundles, connections, and curvature; derive gauge-invariant Lagrangians and Yang–Mills field equations via the principle of least action; analyze free Dirac fields and their gauge interactions in a geometric framework; and discuss the geometric unification of gauge fields with gravitation.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | They are competent in the fundamentals of Physics and in the subfield of their thesis work. | ✔ | |||
| 2 | They have necessary skills (literature search, experiment design, project design, etc.) for doing research with guidance of a more experienced researcher. | ✔ | |||
| 3 | They can communicate research results in a proper format (journal article, conference presentation, project report etc.) | ✔ | |||
| 4 | They can learn necessary skills and techniques (theoretical, experimental, computational etc.) on their own. | ✔ | |||
| 5 | They have necessary skills to work as team member in a research group. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution