Undergraduate Course: Classical Field Theory (MATH11241)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Classical field theory is a necessary bridge between courses such as classical and quantum mechanics and modern mathematical physics courses such as string theory, quantum field theory, etc. This course will introduce some of the most common field theories that we encounter in physics: scalar field theory, Maxwell's theory, Chern-Simons theory, free string theories. The course will also contain an introduction into the subject of special relativity. |
| Course description |
Gauge theories are the cornerstone of many modern theories of physics such as general relativity, Yang-Mills theory, Chern-Simons theories, string theory, etc. These are examples of field theories that have rather special properties. In this course we will study examples of gauge theories from a Lagrangian and a Hamiltonian perspective. We will study Noether's theorem and the associated continuous symmetries, the role of gauge generators in the Hamiltonian formalism, the notion of large gauge transformations and charges associated with the latter. These concepts will be illustrated by studying examples of field theories such as Maxwell's theory, Chern-Simons theories and the description of free closed bosonic strings.
The course will include the following topics:
-Lagrangians for scalar and gauge fields
- Noether's theorem and continuous symmetries
- Hamiltonian description of field theories: first and second class constrained systems.
- Poisson and Dirac brackets.
- Charges and large gauge transformations.
- Maxwell's theory.
- Chern-Simons theories.
- Hamiltonian description of free particles and free closed bosonic strings.
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
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| Academic year 2024/25, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 18,
Supervised Practical/Workshop/Studio Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
73 )
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Coursework 20%, Examination 80% |
| Feedback |
Not entered |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- Construct Lagrangians and identify global and local symmetries for many of the most important physical theories.
- Construct conserved currents using Noether's theorem.
- Identify gauge symmetries.
- Construct Hamiltonians for theories with gauge symmetries and compute boundary charges using the generators of the gauge symmetries.
- Compute with Poisson brackets in field theory.
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Reading List
The course will be based on lecture notes. Recommended in addition to materials provided:
- (**) Classical Electrodynamics, Jackson
- (**) The Classical Theory of Fields, Course of Theoretical Physics, Volume 2, Landau and Lifshitz
- (*) Quantization of Gauge Systems, Henneaux and Teitelboim
- (*) Classical Field Theory, Horatiu Nastase
- (*) Electricity and Magnetism for Mathematicians, Garrity
(*) are available to download from the University Library
(**) copies available in the University Library |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | CFTh,Gauge theory,Chern-Simons theory,strings |
Contacts
| Course organiser | |
Course secretary | |
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