# PHYSICS 746 : Relativistic Quantum Mechanics and Field Theory

## Science

### Course Prescription

Examines quantum field theory. Covers the relativistic generalisations of the Schrödinger equation and many-particle quantum mechanics, quantum electrodynamics is explored using Feynman diagram techniques. Extensions of scalar field theory to include path integrals, statistical field theory, broken symmetry, renormalisation and the renormalisation group.

### Course Overview

This course introduces quantum field theory. It begins with the relativistic generalisations of the Schrödinger equation and many-particle quantum mechanics. Lagrangian field theory is then introduced and applied to the classic examples of the Klein-Gordon, Dirac, and electromagnetic fields. Interactions are considered and Feynman diagrams introduced. Finally, symmetry breaking and gauge fields are examined in the context of the highly topical Goldstone and Higgs models.

### Course Requirements

Restriction: PHYSICS 706, 755

### Capabilities Developed in this Course

 Capability 3: Knowledge and Practice Capability 4: Critical Thinking Capability 5: Solution Seeking Capability 6: Communication
Graduate Profile: Master of Science

### Learning Outcomes

By the end of this course, students will be able to:
1. Describe, discuss, and utilise the Klein-Gordon and Dirac equations and their solutions (Capability 3 and 6)
2. Understand and use bosonic and fermionic field operators and the formalism of second quantisation (Capability 3)
3. Explain and apply the Lagrangian formulation of the theory of fields (Capability 3, 5 and 6)
4. Explain the concept of symmetry and Noether's theorem (Capability 3, 4 and 6)
5. Understand and explain the canonical quantisation of the Klein-Gordon, Dirac, and electromagnetic fields (Capability 3 and 6)
6. Show that the role of propagators and Feynman diagrams are related (Capability 3 and 4)
7. Understand and describe the derivation of the scattering (S) matrix for interacting systems (Capability 3 and 6)
8. Understand and use Wick's theorem relating time-ordered and normally-ordered operator products (Capability 3 and 5)
9. Understand and use Feynman diagrams and rules to compute scattering amplitudes (Capability 3 and 5)
10. Show how broken symmetry leads to the Higgs mechanism (Capability 3)

### Assessments

Assessment Type Percentage Classification
Assignments 40% Individual Coursework
Final Exam 60% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8 9 10
Assignments
Final Exam

### Tuākana

Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html

### Special Requirements

None

This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

For this course, you can expect 20 hours of lectures, 10 hours of tutorials, 40 hours of reading and thinking about the content and 50 hours of work on assignments and preparation of a presentation.

### Delivery Mode

#### Campus Experience

Attendance is expected at scheduled activities including lectures and tutorials.

The course will not include live online events including lectures and tutorials.

Attendance on campus is required for the exam.

The activities for the course are scheduled as a standard weekly timetable.

### Learning Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

The lecturer(s) will provide their own notes for the course. There is no text book, but recommended reading is F. Mandl and G. Shaw, Quantum Field Theory (1984, 2nd edn. 2010), which is probably the single book closest in style and coverage to this course.

### Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

Relevant examples at varying levels of complexity will be presented in tutorials, where students will also be encouraged to contribute.

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

### Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.

The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

### Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website

### Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page .

This should be done as soon as possible and no later than seven days after the affected test or exam date.

### Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

### Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter .

### Disclaimer

Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 31/10/2023 10:53 a.m.