This advanced third year physics course provides an introduction to the concepts and tools of quantum field theory (QFT) and to its applications in various fields, such as particle physics and condensed matter. QFT is arguably the most far-reaching attempt to combine special relativity and quantum physics in a unique framework. This course builds on the content of previous courses on Classical and Quantum Mechanics, Electromagnetism, and Statistical Physics, providing an elegant synthesis of these key areas of modern Physics. We explain in this course the origin of particles (why are all electrons identical?), forces (why same charge repel while gravitation is attractive?) and antiparticles. The Feynman path integral formalism is used, leading to Klein-Gordon, Maxwell and Dirac equations. Feynman diagrams to describe interacting fields are also introduced. The concepts of Gauge Invariance, spontaneous symmetry breaking, as well as the Goldstone and Higgs mechanisms are introduced in a general context, and applied, e.g., to describe superfluidity, superconductivity and ferromagnetism.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Describe the reasons for the failure of relativistic quantum mechanics, such as the causality problem, and the need for quantum field theory
2. Describe the origin of particles and forces
3. Analyse the statistical distributions of identical particles and the repulsive/attractive nature of the forces as a function of spins
4. Apply Feynman rules to calculate probabilities for basic processes with particles (decay and scattering)
5. Obtain classical and/or non-relativistic limits of fully quantum and relativistic models, and identify the relativistic origin of effects such as the spin-orbit interaction
6. Use effective field theory techniques to develop models at large scales
7. Describe qualitatively effects such as superconductivity, superfluidity, and ferromagnetism using the concepts of gauge invariance, Goldstone and Higgs mechanism, and spontaneous symmetry breaking.
8. Apply mathematical tools such as complex analysis, Gaussian path integration, and Fourier analysis in the context of physical systems
9. Develop computational skills by solving numerically simple problems such as pionless effective field theory and the Ising model.
10. Develop oral and written communication skills

Recommended Resources

- Zee, A. (2010) Quantum Field Theory in a Nutshell (2nd ed.), Princeton University Press

- Peskin, M. and Schroeder, D. (1995) An Introduction to Quantum Field Theory, Westview Press, USA

- Lancaster, T. and Blundell S. J. (2014) Quantum ?eld theory for the gifted amateur, Oxford U. Press

- Srednicki, M. (2007) Quantum Field Theory

- Schwartz, M. D. (2013) Quantum Field Theory and the Standard Model, Cambridge U. Press

- Weinberg, S (1995) The Quantum Theory of Field, Vol. 1, Cambridge U. Press

Recommended student system requirements 

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments
• feedback to whole class, groups, individuals, focus group etc

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Lorentz transformations. Relation between spin and statistics.
2	Classical Field Theory Introduction and motivations for QFT. Klein-Gordon, Maxwell, Schrödinger Lagrangians. Least action principle. Euler-Lagrange equations. Symmetries and Noether theorem. Canonical momentum and Hamiltonians.	Skills learned: Mathematical: Complex analysis. Functional integration. Stationary phase approximation. Modelling real systems: Particle physics, atomic nuclei, condensed matter.
3	The Klein-Gordon ?eld Free scalar ?elds. Canonical quantization. Vacuum energy (Casimir e?ect). Cosmological constant. Particles and antiparticles from excitation of the vacuum. Causality problem.
4	Functional method Path-integral formulation of QM. Stationary phase approximation. Generating functional. Functional derivation and integration Correlation functions. Time ordering. Propagator. Residue theorem. Yukawa potential.
5	Interacting ?elds f4 and cubic theories. Gaussian functional integral. Feynman diagrams. S-matrix. Scattering amplitude. Decay.
6	Fermions Elements of group theory. Dirac equation. Yukawa theory.
7	Quantum electrodynamics Electromagnetic tensor. Maxwell equations. Gauge invariance. Lorentz and Coulomb gauges. Basic QED processes.
8	Spontaneous symmetry breaking Goldstone mechanism. Spontaneous symmetry breaking. Higgs mechanisms. Higgs boson. Super?uidity. Superconductivity.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignments	50 %	*	*	1,2,3,4,5,6,7,8,9,10
Final exam	50 %	03/11/2022	01/12/2022	1,2,3,4,5,6,7,8

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

One three hour workshop per week (with online lecture material), and optional weekly tutorial.

Workshops are in person.

Examination(s)

Please note, that where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Assessment Task 1

Assignments

There will be 10 weekly assignments. Some assignments might contain computational works and video presentations.

There are 10 assignments due over the semester. It is intended that the marked assignments will be returned within one week after submission. Further details can be found on the Course Wattle site.

Assessment Task 2

Final exam

There will be a final exam exam. Please refer to the PHYS3201 Wattle page and Examinations timetable for exam scheduling.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

Individual assessment tasks may or may not allow for late submission. Policy regarding late submission is detailed below:

• Late submission permitted. Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 5 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Assignments will be submitted in Wattle.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

No resubmission permitted as the solution is posted online.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students