Expanded notes

At the request of some students, I have added a large appendix on gamma-matrices and their representations, discrete symmetries of the Dirac equation, Majorana and Weyl spinors and corresponding representations etc. I consider all this to be part of QFT I. The expanded notes have been uploaded. All the errors that people have pointed out so far, have been corrected (but there could always be new errors, so please keep looking!).

In particular I have explained the principles behind each of the gamma-matrix representations and provided a method to construct and verify each class of representations from first principles. For some reason most textbooks don't really explain this, so I hope this material will be useful.

Sign error in problem set etc

In the problem set given out recently, there was a typo in the third relation, namely a missing minus sign. The correct relation is:

{\bar\psi} \gamma^\mu \lambda = - {\bar\lambda} \gamma^\mu \psi

This is in fact the reason why {\bar\psi} \gamma^\mu \psi vanishes in the Majorana case, consistent with the fact that there should be no charge current in this case.

Also, there has been a request to include details about charge conjugation and Majorana matrices, and also another request to explicitly put in the various gamma-matrix representations in the notes. I will do these things next week.

Some announcements: Wednesday lecture time/venue, Quiz on 25th.

Starting tomorrow (24 Jan) we will have lectures on most Wednesdays at 4:00 PM in LHC room 305, in addition to the Tuesday and Thursday slots. The detailed schedule and plan of the course up to mid-semester has been updated on the blog page.

Quiz 1 will take place this Thursday Jan 25 in the regular classroom slot (4:00 PM). The duration is 55 minutes starting from exactly 4:00 PM. This quiz (and all other evaluations for this course) will be open-notes: you may use my class notes in any form, digital or printout, including on your mobile phone. However no material other than my class notes is permitted. 

(If anyone chooses to break this trust then the evaluation system for this course may have to be changed, which will affect everyone.)

The lecture notes for this course are available at this link, which is public (anyone can access it). Please let me know in the Comments if you have any difficulty downloading them.

Updated course plan

1. Tuesday 02/01/24 4:00-5:00 PM, 304.
Classical scalar fields and their symmetries.

2. Thursday 04/01/24 4:00-5:00 PM, 304 

More on classical scalar fields and symmetries. 

3. Monday 08/01/24 2:00-3:00 PM, 305

Classical scalar fields and symmetries: nonlinear sigma models.

4. Tuesday 09/01/24 4:00-5:00 PM, 304 

Principal chiral model, Euclidean continuation of field theory.

5. Thursday 11/01/24 4:00-5:00 PM, 304 

Fermion fields, anti-commutation, Grassman numbers.

6. Monday 15/01/24 2:00-3:00 PM, 305 

Symmetries of fermion Lagrangians, chiral symmetry.

7. Tuesday 16/01/24 4:00-5:00 PM, 304 

Vector fields, gauge invariance and gauge fixing.

8. Tuesday 23/01/24 4:00-5:00 PM, 304 

More on vector fields, gauge invariance and gauge fixing. 

9. Wednesday 24/01/24 4:00-5:00 PM, 305

Yang-Mills Lagrangian and non-abelian gauge invariance. 

 

Thursday 25 January: Quiz 1 (based on material from Lectures 1-7)

10. Tuesday 30/01/24 4:00-5:00 PM, 304 

Path integral in quantum mechanics.

11. Wednesday 31/01/24 4:00-5:00 PM, 305 

Path integral in quantum mechanics: methods and examples (i).

12. Thursday 01/02/24 4:00-5:00 PM, 304 

Path integral in quantum mechanics: methods and examples (ii).

13. Tuesday 06/02/24 4:00-5:00 PM, 304 

Path integrals in quantum mechanics: imaginary time and tunneling. 

14. Wednesday 07/02/24 4:00-5:00 PM, 305

Tutorial (will not be video recorded)

15. Thursday 08/02/24 4:00-5:00 PM, 304 

Path integrals in field theory: bosons

16. Tuesday 13/02/24 4:00-5:00 PM, 304 

 Path integrals in field theory: fermions. 

17. Wednesday 14/02/24 4:00-5:00 PM, 305

Path integrals in field theory: bosons/fermions. 

18. Thursday 15/02/24 4:00-5:00 PM, 304 

Path integrals in field theory: gauge fields. 

Mid-semester exam: 23/02/24, 10:00 AM - 12:00 Noon

Problem set uploaded (revised)

The problem set has been uploaded to the same folder where you find the class notes. 

EDIT: At 5:58 PM today (Wednesday) I revised it slightly. The revised version is in a file called 2024-01-17-Problem-set I - revised.pdf. If you have previously downloaded the original, please delete that and use the revised version.

New scheduling issue: please respond

 I have just found out that one registered student of PH 4413/6473 is not available on Mondays at 2 PM. Since it is already late, I am going ahead with today's class. But from next week onwards we will not use the Monday 2 PM slot.

To find a replacement for it, I need to know whether you are all free on Wednesday afternoons: 2-3 PM or 3-4 PM or 4-5 PM. Please indicate your availability by replying to this post in the following format:

Wed 2-3 PM: Yes/No (choose one)

Wed 3-4 PM: Yes/No (choose one)

Wed 4-5 PM: Yes/No (choose one)

This poll is applicable for all Wednesday afternoons till the end of the semester, though I probably won't be using all these extra slots.

All registered students for my course should respond as soon as possible. Students who are auditing regularly may also reply, but please mention "Auditing" in your reply.

Scheduling updates

Some scheduling updates:

• There will be a lecture today, Jan 15, at 2:00 PM in room 305, LHC. 
• Tomorrow, Jan 16, there will as usual be a lecture at 4:00 PM in room 301, LHC.
• However there will be NO lecture on Thursday Jan 18. Instead I will post a Home Assignment on this blog page by Wednesday. This will not be counted towards your course marks, so it is optional. But I request everyone to please do it and submit it to me by email before Saturday night. This will help me understand how the course is going, so it is important to all of us.

Correction of typos

Please bring typos in the notes to my attention. I have corrected all typos I could find so far. Every new version of the notes could have some corrections even in the earlier parts. The single file in the Google Drive will always have the full latest version. 

Today's lecture

 Reminder: There will be a lecture today at 2:00 PM. The room is 305 (confirmed). 

Lecture 1-2 Notes

The Lecture Notes have been updated in the Google Drive folder to  include Lectures 1 and 2. Please note that the updated versions will not only contain new material but they will also have corrections and additions to older material as well as more exercises. So with each update you can replace the old file on your device with the new one.

The video will be uploaded later today. In the future I will not post alerts about updates and uploads of these materials as I plan to do them soon after each lecture.

Course plan, first half of the semester. Please note the Monday lectures and the Quiz.

1. Tuesday 02/01/24 4:00-5:00 PM, 304. 

Classical scalar fields and their symmetries. 

2. Thursday 04/01/24 4:00-5:00 PM, 304 

More on classical scalar fields and symmetries. 

3. Monday 08/01/24 2:00-3:00 PM, 305

Classical scalar fields and symmetries: nonlinear sigma models.

4. Tuesday 09/01/24 4:00-5:00 PM, 304 

Principal chiral model, Euclidean continuation of field theory.

5. Thursday 11/01/24 4:00-5:00 PM, 304 

Fermion fields, anti-commutation, chiral symmetry.

6. Monday 15/01/24 2:00-3:00 PM, 305 

Vector fields, gauge invariance and gauge fixing.

7. Tuesday 16/01/24 4:00-5:00 PM, 304 

Yang-Mills Lagrangian, gauge invariance. 

8. Tuesday 23/01/24 4:00-5:00 PM, 304 

Yang-Mills Lagrangian: Spontaneous symmetry breaking, Higgs mechanism. 

 

Thursday 25 January: Quiz 1

9. Monday 29/01/24 2:00-3:00 PM, 305 

Path integral in quantum mechanics.

10. Tuesday 30/01/24 4:00-5:00 PM, 304 

Path integral in quantum mechanics: methods and examples.

11. Thursday 01/02/24 4:00-5:00 PM, 304 

Path integrals in quantum mechanics: imaginary time and tunneling. 

12. Monday 05/02/24 2:00-3:00 PM, 305 

Path integrals in field theory: bosons. 

13. Tuesday 06/02/24 4:00-5:00 PM, 304 

Path integrals in field theory: fermions. 

14. Thursday 08/02/24 4:00-5:00 PM, 304 

Path integrals in field theory: bosons/fermions. 

15. Tuesday 13/02/24 4:00-5:00 PM, 304 

Path integrals in field theory: gauge fields. 

16. Thursday 15/02/24 4:00-5:00 PM, 304 

Path integrals in field theory: Yang-Mills theory, Faddeev-Popov ghosts. 

Mid-semester exams: 19/02/24 – 26/02/24

Video playlist

The video recordings of course lectures will be added to this playlist. The first video is already uploaded there.

Another way to reach this playlist is to open YouTube and search for the channel "Sunil Mukhi" where the videos and playlist can be found.

Lecture 1 Notes

The first day's lecture notes are available at this link . Please let me know if you have any difficulty downloading them.

Welcome and Overview

This is the webpage for the course Quantum Field Theory II, PHY 4413/6473 being taught by me at IISER Pune during the January Semester, 2024. 

This page will work like a blog -- older posts at the bottom, newer at the top. All posts are available to read. Students crediting the course should read it regularly. On some days there will be assigned self-study before a given lecture as well as problems to solve after the lecture. 

The course timings and venue are: 

• Regular timings: Tuesday and Thursday, 4:00-5:00 PM

• Some weeks: Monday, 2:00-3:00 PM. (will be announced here when it is happening).

• LHC 304

The goals of the course, and the planned course contents, are given below together with some references. 

Goal: To survey Quantum Field Theory from a perspective that goes beyond operator quantisation and computation of basic amplitudes in perturbation theory. To bring out the deep underlying structure of QFT that provides qualitative and quantitative insight into material phenomena in both particle physics and condensed matter physics. To highlight the role of symmetries, path integrals, semi-classical expansions and renormalisation. 

Course Contents (tentative, may change with time): 

1. Classical field theory: general features of scalar fields, fermion fields, gauge fields and their couplings, with an emphasis on symmetries and representations. Non-Abelian gauge theory. (6 lectures)
2. Path integral: Discretisation approach, Gaussian path integral as a determinant, large-time limit and ground state, correlation functions, semi-classical expansion as saddle- point approximation. (8 lectures)
3. Classical solutions in QFT: Topological sectors and conservation laws. Quantisation of solitons. Solitons as topologically stable particle sectors in QFT. Vortices in Abelian Higgs model. Magnetic monopoles. Instantons and tunneling in quantum mechanics. (8 lectures)
4. Renormalisation: Renormalisation scale, the logic of renormalisation. Renormalisation group equation, physical consequences. (7 lectures)

References: 

• An Introduction to Quantum Field Theory – Peskin and Schroeder 

• Quantum Field Theory and The Standard Model – Matt Schwartz

• Solitons and Instantons - R. Rajaraman

Additional reading:  

• Quantum Field Theory - Itzykson and Zuber

• Lectures of Sidney Coleman on Quantum Field Theory (multiple authors)

• Quantum Field Theory and Critical Phenomena - Jean Zinn-Justin

• David Tong, Statistical Field Theory (Lecture Notes).

        • Gauge Fields and Strings - Alexander M. Polyakov 

I will regularly post my own notes on this blog. The first three books above will also be useful for different parts of the course, while the others are for additional reading.