Generalised symmetries and anomalies: From quantum mechanics to quantum matter
IISER Kolkata
Three lectures of two hours each, connecting generalized symmetries and anomalies from quantum mechanics to quantum matter.
Teaching & mentoring
Learning through questions.
Lecture notes, problem sets and student research—from an introduction to quantum field theory to projects in CFT, gravity and many-body physics.
I have taught introductory quantum field theory and general relativity, delivered lectures on generalized symmetries, and supervised projects connecting modular forms, CFT and gravity. The materials below bring together lecture resources and student work from these programmes.
Courses & lectures
From foundations to calculations.
Physics for Bangladesh — introductory Quantum Field Theory
ICTP Physics Without Frontiers
Six introductory QFT lectures, with lecture notes, problem sheets, worked solutions and recorded lectures.
A minimal introduction to Quantum Field Theory
A 92-page introduction to Lorentz and Poincaré symmetry, classical field theory, Noether’s theorem, canonical quantization, complex scalar fields, causality, and free Dirac fields.
Author: Arpit Das
Quantum Field Theory — Problem Sheet 1
Exercises accompanying the introductory QFT lectures, beginning with Lorentz transformations, classical field equations and the electromagnetic field.
Author: Arpit Das
Quantum Field Theory — Problem Sheet 1: Solutions
Worked solutions to the first QFT problem sheet, with references to the accompanying lecture notes.
Author: Arpit Das
Quantum Field Theory — Problem Sheet 2
Exercises on canonical commutators, translation generators and quantum fields.
Author: Arpit Das
General Relativity and Cosmology
IISER Kolkata
Prepared assignments and notes, conducted tutorials and graded scripts.
A derivation of the FLRW metric
A pedagogical derivation of the cosmological metric from spacetime symmetries and the cosmological principle.
Author: Arpit Das
General Relativity — Problem Set 1
Exercises on Galilean and Lorentz transformations, Maxwell’s equations, and the Minkowski metric.
Author: Arpit Das
General Relativity — Horizons and Surface Gravity
Exercises on null hypersurfaces, event horizons, Killing horizons and surface gravity.
Author: Arpit Das
Student research
Working on questions together.
Projects, supervision and mentoring across institutions. Reports below are credited to their student authors.
Summer internship
Project on the Mathur–Mukhi–Sen classification of rational conformal field theories. 1 student · 3 months.
Modular Forms in Physics
Summer internship report introducing modular forms and their applications in physics, supervised by Arpit Das.
Student author: Yash C. Patki
EPSRC Vacation Scholarship
Project on the Mathur–Mukhi–Sen classification of rational conformal field theories. 1 student · 2.5 months.
Three-Character MLDEs in the j-Plane: Wronskian Structure and Index Constraints
Supervised project studying third-order modular differential equations in the modular invariant j, Wronskians and local no-logarithm constraints.
Student author: Anxu Gao
Physics for Bangladesh internships
Projects on the Mathur–Mukhi–Sen classification of rational CFTs and on generalized symmetries, anomalies and hydrodynamics. 4 postgraduate projects · 3 months per project.
Generalized Global Symmetries in QFT
Internship report on ordinary and higher-form symmetries, Ward identities, spontaneous symmetry breaking and Maxwell theory.
Student author: Md. Samim-ul-Islam
MIORPA — Mathematical Institute’s Online Research Projects with Africa
Projects on the Mathur–Mukhi–Sen classification of rational conformal field theories. 2 students · 2 months per project.
Application of Modular Forms in Physics
Introductory study of modular forms, Eisenstein series, modular derivatives, the Klein j-invariant and modular linear differential equations.
Student author: Segun Olofin Akerele
Classifying rational conformal field theories / vertex operator algebras using modular linear differential equations
Supervised project report on the Mathur–Mukhi–Sen approach to low-rank RCFT characters using modular forms and MLDEs.
Student author: Fobasso Djousse Keplaire
Semester projects in a QFT course
Supervised projects on Hawking radiation and black-hole thermodynamics. 8 students.
Research mentoring
Mentored postgraduate and graduate students and postdoctoral researchers in high-energy theoretical physics.
More on the blackboard.
Browse the broader collection of study notes, calculations and presentation slides, or get in touch about an academic discussion.