# Mathematics / Applied Mathematics MSc

# 5M: Classical Field Theory MATHS5054

**Academic Session:**2019-20**School:**School of Mathematics and Statistics**Credits:**20**Level:**Level 5 (SCQF level 11)**Typically Offered:**Either Semester 1 or Semester 2**Available to Visiting Students:**No**Available to Erasmus Students:**No

#### Short Description

The course is a mathematical introduction to one of the pillars of modern physics - special relativity - together with an introduction to the construction of relativistic field theories.

#### Timetable

2 hours of lectures a week, over 11 weeks.

1 hour tutorial a week over 10 weeks (or equivalent)

#### Requirements of Entry

Mandatory Entry Requirements

Recommended Entry Requirements

MATHS4107 - 4H: Mathematical Physics

#### Assessment

Assessment

100% Final Exam

Reassessment

In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

**Main Assessment In:** April/May

**Are reassessment opportunities available for all summative assessments?** No

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

#### Course Aims

The aim of this course is to give a mathematical introduction to classical field theory by extending the Lagrangian and Hamiltonian formalism of particle mechanics (introduced in 4H: Mathematical Physics) to fields. The main example will be the treatment of Maxwell's theory of electromagnetism as a Lagrangian field theory; this will include the study of the Lorentz group and special relativity. Other examples that will possibly be covered during the course are the Klein-Gordon and Einstein's field equations of general relativity as well as a discussion of special solutions such as electromagnetic and gravitational waves.

#### Intended Learning Outcomes of Course

By the end of this course students will be able to:

1. Explain the basic principles and properties of the Lagrange and Hamilton formalism of field theory, for example the derivation of field equations and the discussion of some of their solutions as well as their interpretation.

2. Explain the concept of symmetries and apply Noether's theorem to derive conservation laws and the energy momentum tensor.

3. Discuss the invariance of Newtonian dynamics and nonrelativistic field theory under Galilean transformations and be able to define the Galilean Group.

4. Apply the general formalism of Outcomes 1 and 2 to the theory of electromagnetism; in particular, derive the electromagnetic field equations, the electromagnetic energy-momentum tensor and discuss the invariance of the theory under Lorentz transformations.

5. Explain the basic principles of Einstein's special theory of relativity and perform calculations in Minkowski space-time with 4-tensors under the Lorentz Group.

6. Discuss other examples of relativistic field equations, such as the derivation of the Klein-Gordon equation and/or the Dirac equation and/or Einstein's field equations as well as their Lorentz transformation properties.

#### Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.