NPTEL Course: Field Theory - Classical, Quantum, Equilibrium & Nonequilibrium | Prof. Mahendra Verma

Course Details

Tapestry of Field Theory: Classical & Quantum, Equilibrium & Nonequilibrium Perspectives

Field theory stands as one of the most powerful and unifying frameworks in modern theoretical physics. It provides the language for describing systems with infinite degrees of freedom, from the fundamental particles governed by quantum fields to the emergent phenomena in complex statistical systems. Yet, the connections between its various branches—quantum, statistical, classical, and nonequilibrium—are often taught in isolation.

This 12-week NPTEL course, "Tapestry of Field theory: Classical & Quantum, Equilibrium & Nonequilibrium Perspectives," taught by the distinguished Prof. Mahendra Verma of IIT Kanpur, aims to weave these disparate threads into a single, coherent canvas. Designed for postgraduate and advanced undergraduate students, the course offers a rare breadth-first perspective, comparing and contrasting the core paradigms that shape our understanding of the physical world.

About the Instructor: Prof. Mahendra Verma

Prof. Mahendra Verma is a leading authority in computational and theoretical turbulence and parallel computing. A professor in the Department of Physics at IIT Kanpur, his contributions are both deep and wide-ranging:

• Pioneering Research: His group has developed seminal simulation codes like TARANG (for hydrodynamics, magnetohydrodynamics, convection), SARAS, and QuantTARANG.
• Accolades: A recipient of the prestigious J.C. Bose Fellowship, Swarnajayanti Fellowship, Dr. A.P.J. Abdul Kalam Cray HPC Award, and the INSA Teacher Award.
• Leadership: A fellow of all three major Indian science academies: INSA, IASc, and NASI.
• Author: He has authored several influential books, including "Energy Transfers in Fluid Flows."

Prof. Verma's unique expertise, bridging high-performance computation, turbulence, and field-theoretic methods, makes him the ideal guide for this integrative course.

Course Overview and Objectives

This course is built on a compelling premise: that a unified view of field theory enriches a physicist's perspective. It moves beyond traditional silos to highlight the shared mathematical structures and conceptual tools.

Key Themes Include:

• The foundational tools of Lagrangian/Hamiltonian formulations, functional integrals, and Green's functions.
• Core principles of Quantum Field Theory (QFT), including second quantization, Feynman diagrams, and gauge theories like QED.
• Essentials of Statistical Field Theory (SFT), covering Landau theory, mean-field approaches, and the powerful framework of the Renormalization Group (RG).
• The extension of field-theoretic methods to nonequilibrium systems, such as dynamical critical phenomena, the KPZ equation, and the Time-Dependent Ginzburg-Landau equation.
• A culminating application: Field Theory of Turbulence, where Prof. Verma's research shines, covering hydrodynamic, Euler, scalar, and magnetohydrodynamic turbulence.

Who Should Enroll?

Intended Audience: Masters and PhD students in Physics, as well as advanced undergraduate students with a strong foundation.

Prerequisites: A solid background in Quantum Mechanics, Statistical Physics, and Mathematical Methods is essential. Familiarity with the following NPTEL courses is recommended:

• Introductory Quantum Mechanics
• Mathematical Methods and its Applications

Detailed 12-Week Course Layout

Recommended Textbooks & Resources

• Lancaster and Blundell, Quantum Field Theory for the Gifted Amateur (Oxford).
• Peskin and Schroeder, An Introduction To Quantum Field Theory (CRC Press).
• M. K. Verma, Energy Transfers in Fluid Flows (Cambridge Univ. Press, 2019).
• W. D. McComb, Homogeneous, Isotropic Turbulence (Oxford Univ. Press, 2014).
• Seminal articles by Hohenberg & Halperin and M.K. Verma will be referenced.

Why This Course is Unique

This course is not just another syllabus on field theory. It is a deliberate synthesis. By placing quantum field theory, statistical field theory, and classical nonequilibrium field theory side-by-side, it allows students to see how techniques like path integrals, renormalization, and symmetry breaking recur and adapt across domains. The final weeks dedicated to turbulence are a masterclass in applying these abstract tools to one of physics' most challenging unsolved problems, directly from a world expert.

For any aspiring theorist in particle, condensed matter, statistical, or fluid physics, this course offers an invaluable opportunity to build a holistic and powerful intellectual toolkit, guided by one of India's most accomplished physicists.

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