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Faculty Handbook 2022-2023

# Module Description

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

## Department: Mathematical Sciences

### MATH4061: ADVANCED QUANTUM THEORY IV

Type Level Credits Availability Module Cap Open 4 20 Available in 2022/23 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).

• None.

• None.

#### Aims

• The module is intended as an introduction to Quantum Field Theory bringing together concepts from Lagrangian and Hamiltonian mechanics and special relativity. It discusses both free and interacting theories.
• It also provides an elementary introduction to string theory, developing the subject sufficiently to determine the spectrum and identify certain symmetries and dualities.

#### Content

• The action principles and the classical Lagrangian formalism of classical field theory.
• Quantisation of free scalar fields.
• Interacting quantum fields.
• Path integrals.
• String theory: the classical theory, the quantum theory, its symmetries and spectrum.
• Renormalisation and renormalisation group flow

#### Learning Outcomes

Subject-specific Knowledge:
• 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 fundamental aspects of string theory (quantisation of free strings, string constraints and their algebraic description, the string spectrum)
• be able to calculate amplitudes and interaction, and understand their scale dependence
Subject-specific Skills:
• students will be able to use a variety of highly specialised and advanced technical skills in the area of theoretical elementary particle physics
Key Skills:
• students will have developed the ability to operate in complex and specialised contexts close to the cutting edge of current research

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Demonstration through lecturing and the application of theory to practical examples.
• Written assignments providing formative practice in the application of logic, rigour and extended discourse.
• Summative examinations assessing these elements, testing the acquired skills involving complex unpredictable and specialised problems in quantum field theory.

#### 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%

#### Formative Assessment:

Eight written or electronic 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