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.