Undergraduate Programme and Module Handbook 2018-2019 (archived)
Module MATH4061: ADVANCED QUANTUM THEORY IV
Department: Mathematical Sciences
MATH4061:
ADVANCED QUANTUM THEORY IV
Type |
Open |
Level |
4 |
Credits |
20 |
Availability |
Available in 2018/19 |
Module Cap |
|
Location |
Durham
|
Prerequisites
- (mathematics modules to the value of 100 credits in Years 2
and 3, with at least 40 credits at Level 3, and including Quantum
Mechanics III (MATH3111)) OR (mathematics modules to the value of 100
credits in Years 2 and 3, with at least 40 credits at Level 3, and
including Theoretical Physics 2 (PHYS2631) or Foundations Of Physics 3A
(PHYS3621).
Corequisites
Excluded Combination of Modules
Aims
- The module is intended as an introduction to Quantum Field Theory
using strings as a primary example
- It also develops string theory sufficiently to show that its
spectrum includes all elementary particles thus unifying the fundamental
forces
Content
- The syllabus contains: Action principles and classical
theory
- Quantisation of free scalar fields; application to
strings
- Virasoro algebra: string constraints as generators of
conformal transformations, representations, central
charge
- Spectra: physical state condition, no-ghost theorem,
critical dimension, open string spectrum. Connection to gauge theory,
non-Abelian gauge symmetry and importance for the Standard Model. Closed
string spectrum, connection to Gravity. Compactification.
- Spinning string: gauge-fixed action, Ramond and
Neveu-Schwarz boundary conditions, Super-Virasoro algebra,
spectrum
- Dirichlet branes
Learning Outcomes
- Having studied the module students will know the basic
principles of quantum field theory and the role of symmetry in modern
particle physics.
- be familiar with the fundamental aspects of string theory
(quantisation of free strings, string constraints and their algebraic
description,spectrum)
- have been made aware of the connection between string spectra
and the Standard Model.
- students will be able to use a variety of highly specialised
and advanced technical skills in the area of theoretical elementary
particle physics
- students will have developed the ability to operate in
complex and specialised contexts close to the cutting edge of
research
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lecturing demonstrates what is required to be learned and the
application of the theory to practical examples.
- Written assignments provide formative practice in the
application of logic, rigour and extended discourse.
- Summative examinations assess these elements, the knowledge
acquired and the ability to solve complex unpredictable and specialised
problems.
Teaching Methods and Learning Hours
Activity |
Number |
Frequency |
Duration |
Total/Hours |
|
Lectures |
42 |
2 per week for 20 weeks and 2 in term 3. |
1 Hour |
42 |
|
Problems Classes |
8 |
Four in each of terms 1 and 2 |
1 Hour |
8 |
|
Preparation and Reading |
|
|
|
150 |
|
Total |
|
|
|
200 |
|
Summative Assessment
Component: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
Written examination |
3 Hours |
100% |
|
Eight written assignments to be assessed and
returned. Other assignments are set for self-study and complete solutions
are made available to students.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University