This is a course on quantum field theory for PhD students.
Meetings: Th (1430–1630h) — F (1430–1630h) in Lecture Hall H
Grading: Report + Presentation: 70%, Internal Assessment: 30%
Office Hours: By appointment only.
This course has as a prerequisite PH-ET536 and PH-ET576, our QFT I and QFT II electives offered to MSc students.
A tentative list of topics to be covered may be viewed here. The choice of topics is flexible and this list is meant only to be indicative, both of the planned scope and the prerequisites implied.
02/16: No class this week, i.e. 20th and 21st February. Please submit topics you'd like to write your report on before our next meeting.
16. Monopoles — 04/25
15. Lattice Fermions — 04/24
14. Instantons — 04/17
13. Lattice Gauge Theory — 04/09
12. Gauge Anomalies and Anomaly Cancellation — 03/28
11. Background Field Method — 03/28
10. The Chiral Anomaly — 03/26
9. Soft Collinear Effective Field Theory — 03/21
8. 1-Loop β-Function for Non-Abelian Gauge Theories — 03/20
7. IR Divergences — 02/14
6. Basics of Thermal Field Theory — 02/13
5. BRST Quantisation — 02/07
4. Local Symmetries, Constraints, and Quantisation — 02/06
3. Weinberg's Soft Photon Theorem — 01/31
2. Wigner's Classification and Little Groups — 01/24
1. Coherent States in Quantum Mechanics — 01/23
You will best be served by going over the discussion of any topic from more than one of the following non-exhaustive list of references. There are also plenty of excellent lecture notes on (various aspects of) quantum field theory you can find on the arXiv.
Itzykson & Zuber — Quantum Field Theory
Mandl & Shaw — Quantum Field Theory
Peskin & Schroeder — An Introduction to Quantum Field Theory
Ramond — Field Theory: A Modern Primer
Schwartz — Quantum Field Theory and the Standard Model
Sterman — An Introduction to Quantum Field Theory
Zinn-Justin — Quantum Field Theory and Critical Phenomena
Weinberg — The Quantum Field Theory of Fields (Vols. I and II)
More references specific to the topic of discussion will be provided as we go along.
This is the second of a two-semester sequence of courses on quantum field theory.
Course Code: PH-ET576
Meetings: Th (1330–1430h and 1630–1730h) — F (1330–1430h and 1630–1730h) in Lecture Hall 9
Grading: Final Exam: 70%, Internal Assessment: 30%
Office Hours: By appointment only.
Working chiefly in the path integral formalism, we studied more advanced aspects of quantum field theory including renormalisation, and effective field theories. The plan was to cover non-Abelian gauge theories, too, we didn't have enough time to get to it.
04/28: We're done with lectures for this semester. Your final exams are on 28th May. Good luck!
04/11: I've fallen quite ill. Today's classes are cancelled.
03/27: Your mid-term papers have been corrected. I will discuss your answer scripts in class on 27th March (1630–1730h).
03/20: The feedback form for the course is available here. Please fill it up some time in the coming month.
02/25: The internal assessment test is scheduled for Tuesday, 18th March between 1600–1730h.
02/16: No classes this week, i.e. 20th and 21st February.
01/12: Sorry for the frequent announcements regarding the schedule. Please see above for the tentative schedule for the coming weeks.
01/08: There will be no class today. For the rest of this week, we will meet in Lecture Hall 9 on Thursday and Friday (1330-1430).
01/05: The notes for each class can be downloaded by clicking on the lecture title.
01/02: The class timings above are indicative, as the time-table is not yet finalised. On January 3rd, however, we will have class from 1330–1530h in Lecture Hall 9.
01/02: The course information sheet is here.
Assignments will not be counted as part of your internal assessment grade, but can be submitted for evaluation and feedback provided they adhere to the guidelines.
26. Abelian Higgs Models, Superconductors, and Confinement — 04/25
25. Effective Field Theories for Nambu-Goldstone Modes — 04/24
24. Spontaneous Symmetry Breaking in Yukawa Theory — 04/17
23. Lie Algebras — 04/04
22. All Together Now — 04/03
21. Wilsonian RG — 03/28
20. RG Flows II — 03/27
19. RG Flows — 03/21
18. RG Equations — 03/20
17. Renormalisation of QED II — 03/07
16. Renormalisation of QED I — 03/06
15. Renormalisation of Quartic Scalar Theory — 02/28
14. Counting UV Divergences — 02/27
13. Anomalous Magnetic Moment — 02/14
12. On-Shell Subtraction — 02/13
11. Electron Self-Energy Graphs — 02/07
10. Vacuum Polarisation in QED — 02/06
9. Dimensional Regularisation — 01/31
5. Lehmann-Symanzik-Zimmermann Reduction — 01/17
4. Dyson-Schwinger Revisited — 01/16
3. Dyson-Schwinger, Canonically — 01/10
2. Path Integrals for Gauge Fields — 01/09
1. Path Integrals for Scalars — 01/03
There are many, many textbooks on quantum field theory. Below is a small selection of references that adopt the same conventions as we do in the lectures. You should skim through these (and other!) texts and find one that suits your tastes.
Das — Field Theory: A Path Integral Approach
Itzykson & Zuber — Quantum Field Theory
Mandl & Shaw — Quantum Field Theory
Peskin & Schroeder — An Introduction to Quantum Field Theory
Ramond — Field Theory: A Modern Primer
Schwartz — Quantum Field Theory and the Standard Model
Sterman — An Introduction to Quantum Field Theory
Zee — Quantum Field Theory in a Nutshell
Zinn-Justin — Quantum Field Theory and Critical Phenomena
There are also many excellent lecture notes available online:
Finally, for background reading, I recommend:
Cao (Ed.) — Conceptual Foundations of Quantum Field Theory
Schweber — QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga
Between August–November 2024, I taught the first of a two-semester sequence of courses on quantum field theory. The course was divided into roughly four parts: (i) canonical and path integral quantisation of free scalar fields, (ii) spinors, Abelian gauge fields, and their quantisation, (iii) interactions and tree-level scattering amplitudes in various theories, and (iv) spontaneous symmetry breaking. It was planned initially that we would also discuss some aspects of the large-N approximation and lattice field theory, but this was not possible.
The final examination for the course is scheduled for 12th December between 10 AM – 1 PM.
We're done with lectures for the semester, so good luck for your final exams!
In light of the Delhi U. notification, classes on 21st and 22nd November will be held online.
The feedback form is available here. Please be sure to fill it before the end of this month!
The class on Friday, October 25th between 830–10h will be taken by DC for the particle physics course.
Due to the NAAC visit, DC and I will exchange classes. There will be a QFT class on Wednesday, October 23rd between 830–10h. The particle physics class that usually takes place at this time will be moved to either Thursday or Friday morning, please check this page again for an update!
On October 17th and 18th, Prof. Debajyoti Choudhury (DC) will teach the module on spontaneous symmetry breaking at the regular class timings.
The midterm examination is scheduled for October 22nd, 2024 at 3:00 PM.
In light of the Delhi U. notification regarding the Delhi University Students' Union elections, both classes on Friday, 27th September are cancelled.
PhD students crediting this course are required to do a project worth two credits in addition to the requirements for Masters students. They are requested to send me an e-mail indicating their name, their PhD advisors name, and their prospective area of research.
Based on the revised time-table (w.e.f. 12th August), classes will henceforth be held on Thursdays and Fridays!
The course information sheet is available here.
30. QED — 11/22
29. Scalar QED — 11/21
28. Where Do Feynman Rules Come From? — 11/14
27. Scattering in Theories with Fermions — 11/08
26. More Amplitudes — 11/07
25. Scattering Amplitudes in Scalar Theories — 10/25
24. The S-Matrix and Decay Amplitudes — 10/24
23. Spontaneous Symmetry Breaking II — 10/18
22. Spontaneous Symmetry Breaking I — 10/17
21. Interactions — 10/11
20. Gupta-Bleuler — 10/10
19. Maxwell Theory — 10/04
18. Path Integrals for Dirac Fermions — 10/03
17. Propagators — 09/26
16. Spin-Statistics Connection — 09/20
15. Dirac Lagrangian — 09/19
14. Dirac Lagrangian — 09/13
13. What is a Spinor? — 09/12
12. The Lorentz Lie Algebra — 09/06
11. The Lorentz and Poincare Groups — 09/05
10. Path Integral in Quantum Field Theory — 08/30
9. Path Integral in Quantum Mechanics — 08/29
8. Feynman Propagator and Complex Scalars — 08/23
7. Causality and Propagation — 08/22
6. Mode Expansions and Fock Space — 08/16
5. Canonical Quantisation — 08/10
4. Gauging Global Symmetries — 08/09
3. Noether's Theorem — 08/08
2. Field Theory and Statistical Mechanics — 08/03
1. Classical Scalar Fields — 08/02
There are many, many textbooks on quantum field theory. Below is a small selection of references that adopt the same conventions as we do in the lectures. You should skim through these (and other!) texts and find one that suits your tastes.
Das — Lectures on Quantum Field Theory
Itzykson & Zuber — Quantum Field Theory
Mandl & Shaw — Quantum Field Theory
Peskin & Schroeder — An Introduction to Quantum Field Theory
Ramond — Field Theory: A Modern Primer
Schwartz — Quantum Field Theory and the Standard Model
Sterman — An Introduction to Quantum Field Theory
Zee — Quantum Field Theory in a Nutshell
Zinn-Justin — Quantum Field Theory and Critical Phenomena
There are also many excellent lecture notes available online:
Finally, for background reading, I recommend:
Cao (Ed.) — Conceptual Foundations of Quantum Field Theory
Schweber — QED and the Men Who Made it: Dyson, Feynman, Schwinger, and Tomonaga
This was the second of a two-semester sequence of courses on quantum field theory. (For part one of this course, see below.)
Course Code: PH-ET576
Meetings: Th (830–10h) — F (830–10h) — Sa (830–10h)
Grading: Final Exam: 70%, Internal Assessment: 30%
Office Hours: By appointment only.
Working chiefly in the path integral formalism, we studied more advanced aspects of quantum field theory including non-Abelian gauge theories, renormalisation, spontaneous symmetry breaking, and effective field theories. We were also able to discuss some aspects of quantum field theories in low dimensions.
05/10: There will be no class on Saturday, 11th May! In the meanwhile, the feedback form for the QFT II course is available here.
04/21: Please come review your internal assessment answer scripts in my office between 13:00–14:00 on 22nd—26th April.
04/04: The tentative date for the final examination is Saturday, 8th June '24.
03/21: In light of the recent Delhi U. notification, there will be no classes on 22–23rd March.
03/11: The tentative date and time for the internal assessment test is Tuesday, 2nd April '24 at 4:00 PM.
02/09: Starting this week, Saturday's classes will begin at 8:30 AM.
02/02: On request, in light of the GATE examination, class tomorrow (Saturday, 3rd February) stands cancelled.
01/29: Starting next week (i.e. from 02/05), the class schedule will change to Th (830–10h) — F (830–10h) — Sa (9–10h).
01/28: Regular classes will resume on Monday, 29th January.
01/16: There will be no classes between 22–27th January.
Assignments will not be counted as part of your internal assessment grade, but can be submitted for evaluation and feedback provided they adhere to the guidelines.
38. Vertex Operators and Bosonisation — 05/10
37. Two-Dimensional Fermions, Compact Bosons, and T-Duality — 05/09
36. Abelian Higgs Model — 05/04
35. Effective Field Theories — 05/03
34. Scattering of Nambu-Goldstone Bosons — 05/02
33. Spontaneous Symmetry Breaking — 04/27
32. Monopoles — 04/26
31. Symmetry and Renormalisation — 04/25
30. Feynman Rules — 04/20
29. BRST Symmetry — 04/19
28. Faddeev-Popov for Non-Abelian Gauge Fields — 04/18
27. Effective Field Theory: Not Everything Goes! — 04/13
26. Yang-Mills Theory — 04/12
25. Lie Algebras and Wilson Loops — 04/06
24. Wilsonian Renormalisation Group II — 04/05
23. Wilsonian Renormalisation Group I — 04/04
22. Running Masses and Renormalisation Group Flows — 03/21
21. Renormalisation Group Equations — 03/16b
20. 1-Loop Renormalisation of Quantum Electrodynamics — 03/16a
19. Renormalised Perturbation Theory II — 03/14
18. 1-Loop Renormalisation of 𝜙⁴ Theory — 03/09
17. Renormalised Perturbation Theory I — 03/08
16. Counting UV Divergences — 03/07
15. Anomalous Magnetic Moment — 03/02
14. Pole Mass and Subtraction Schemes — 03/01
13. Electron Self-Energy — 02/29
12. Vacuum Polarisation in Quantum Electrodynamics — 02/24
11. Dimensional Regularisation — 02/23
10. Vacuum Polarisation in Scalar Theories — 02/22
9. A Bird's Eye View of Renormalisation — 02/17
8. Infinities and Regulators— 02/16
7. Takahashi-Ward Identities — 02/15
6. LSZ Reduction — 02/10
5. Dyson-Schwinger, Path Integrally — 02/09
4. Dyson-Schwinger, Canonically — 02/08
3. Path Integrals for Fermions and Abelian Gauge Fields — 02/02
2. Path Integrals for Scalars — 02/01
1. Introduction — 01/29
There are many, many textbooks on quantum field theory. Below is a small selection of references that adopt the same conventions as we do in the lectures. You should skim through these (and other!) texts and find one that suits your tastes.
Das — Field Theory: A Path Integral Approach
Itzykson & Zuber — Quantum Field Theory
Mandl & Shaw — Quantum Field Theory
Peskin & Schroeder — An Introduction to Quantum Field Theory
Ramond — Field Theory: A Modern Primer
Schwartz — Quantum Field Theory and the Standard Model
Sterman — An Introduction to Quantum Field Theory
Zee — Quantum Field Theory in a Nutshell
Zinn-Justin — Quantum Field Theory and Critical Phenomena
There are also many excellent lecture notes available online:
Finally, for background reading, I recommend:
Cao (Ed.) — Conceptual Foundations of Quantum Field Theory
Schweber — QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga
This course was co-taught with Suman Chowdhury (SC).
Course Code: PH-ET583
Meetings: Th (12–13h) — F (12–13h) — Sa (10–12h)
Grading: Final Exam: 70%, Internal Assessment: 30%
Office Hours: By appointment only.
My lectures in this course covered critical phenomena and the renormalisation group.
04/04: The tentative date for the final examination is Monday, 3rd June '24.
01/18: Units I–IV on many-body theory, superconductivity, and superfluidity will be covered by SC, and Units V–VI on critical phenomena and the renormalisation group will be covered by me. My lectures will begin after the internal assessment test.
Assignments will not be counted as part of your internal assessment grade, but can be submitted for evaluation and feedback provided they adhere to the guidelines.
11. Gaussian Fixed Points — 05/10
10. Momentum-Shell Renormalisation Group — 05/09
9. Ginzburg Criterion — 05/04
8. Correlation Length — 05/03
7. Green's Functions — 05/02
6. Path Integrals — 04/27
5. Landau-Ginzburg Theory II — 04/26
4. Landau-Ginzburg Theory — 04/25
3. Landau's Theory of Phase Transitions — 04/20
2. Mean Field Theory, Again — 04/19
1. Ising Model and Mean Field Theory — 04/18
Below is a small selection of references that I have found useful in preparing these lectures. You should skim through these (and other!) texts and find one that suits your tastes.
Goldenfeld — Lectures on Phase Transitions and Critical Phenomena
Kardar — Statistical Physics of Fields
Shankar — Quantum Field Theory and Condensed Matter
Zinn-Justin — Quantum Field Theory and Critical Phenomena
Between September–December 2023, I taught the first of a two-semester sequence of courses on quantum field theory. We discussed the canonical and path integral quantisation of scalars, spinors, and Abelian gauge fields, building up to a study of elementary processes in quantum electrodynamics.
12/25: Although we're done with the syllabus for this semester, I'll be in class on Wednesday, 27th December '23 to answer questions.
12/20: The tentative date for the final examination is Friday, 19th January '24.
12/06: Please fill out the student feedback form before the end of this month!
11/22: Please arrange to come see your mid-term paper in my office during your lunch breaks between 22–24th November, 2023.
11/10: Following the Delhi U. notification dated 11/09, there will be no classes between 13–17th November, 2023.
10/27: In light of internal assessment tests, there will be no class on Wednesday, 1st November '23.
10/23: The internal assessment --- a one-hour closed-book test --- will be held on Friday, 10th November '23. It will count for 25% of your final grade in this course.
09/14: SS and I will be exchanging classes starting next week, i.e. Monday, 18th September '23. The Monday lectures will now be held on Wednesdays at 11 AM. Timings on Thursday and Friday remain unchanged.
Assignments will not be counted as part of your internal assessment grade, but can be submitted for evaluation and feedback provided they adhere to the guidelines.
53. Soft Photons — 12/22b
52. Klein-Nishina and Thomson — 12/22a
51. Compton Scattering — 12/21
50. Photon Polarisation Sums — 12/20
49. Elementary Processes w/ Spin — 12/15b
48. Unpolarised Scattering — 12/15a
47. Signs and Traces— 12/14
46. Light-Matter Interactions— 12/13
45. Gauge Invariance — 12/08b
44. Elementary Processes w/o Spin — 12/08a
43. Scalar Electrodynamics — 12/07
42. Where Do Feynman Rules Come From? — 12/06
41. Amplitudes for Fermions — 12/01b
40. Yukawa Theory — 12/01a
39. Green's Functions — 11/30
38. Cross Sections and Decay Rates — 11/29
37. Amplitudes for Scalars — 11/24b
36. Feynman Rules — 11/24a
35. Scattering Amplitudes — 11/23
34. The S-Matrix and Decay Amplitudes — 11/22
33. Interactions: Dyson's Formula — 11/09
32. Path Integrals for Photons and Introducing Interactions — 11/08
31. Faddeev-Popov — 11/03b
30. Canonical Quantisation of Maxwell Theory — 11/03a
29. Free Maxwell Theory and Gauge Symmetry — 11/02
28. Path Integrals for Fermions — 10/27b
27. Dirac Propagator — 10/27a
26. Canonical Quantisation of Dirac Fields — 10/26
25. Spin-Statistics Theorem — 10/25
24. Inner and Outer Products — 10/20b
23. Plane Wave Solutions to Dirac Equation — 10/20a
22. Weyl and Majorana Spinors — 10/19
21. The Dirac Lagrangian — 10/18
20. Dirac Spinors — 10/13b
19. Spinor Representations — 10/13a
18. Tensor Representations — 10/12
17. Groups and Algebras: Lorentz and Poincaré— 10/11
16. Green's Functions— 10/06b
15. Path Integrals in Field Theory — 10/06a
14. Functional Determinants II: Gel'fand-Yaglom — 10/05
13. Functional Determinants I: Gaussian Fluctuations— 10/04
12. Path Integrals in Quantum Mechanics— 09/29b
11. Complex Scalar Field — 09/29a
10. Propagators — 09/27
9. Lorentz Invariance and Causality — 09/22b
8. Zero-Point Energy and Fock Space — 09/22a
7. Mode Expansions — 09/21
6. Rules for Canonical Quantisation — 09/20
5. How To Gauge a Global Symmetry — 09/15b
4. Noether's Theorem II: Spacetime Symmetries — 09/15a
3. Noether's Theorem I: Internal Symmetries — 09/14
2. Field Theory and Statistical Mechanics — 09/11
1. Classical Scalar Fields — 09/04
There are many, many textbooks on quantum field theory. Below is a small selection of references that adopt the same conventions as we do in the lectures. You should skim through these (and other!) texts and find one that suits your tastes.
Das — Lectures on Quantum Field Theory
Itzykson & Zuber — Quantum Field Theory
Mandl & Shaw — Quantum Field Theory
Peskin & Schroeder — An Introduction to Quantum Field Theory
Ramond — Field Theory: A Modern Primer
Schwartz — Quantum Field Theory and the Standard Model
Sterman — An Introduction to Quantum Field Theory
Zee — Quantum Field Theory in a Nutshell
Zinn-Justin — Quantum Field Theory and Critical Phenomena
There are also many excellent lecture notes available online:
Finally, for background reading, I recommend:
Cao (Ed.) — Conceptual Foundations of Quantum Field Theory
Schweber — QED and the Men Who Made it: Dyson, Feynman, Schwinger, and Tomonaga
This course was co-taught with Debajyoti Choudhury, Nivedita Deo, and Abhass Kumar.