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Syllabus
Classical fields; Functional derivatives; Action principle for fields. Lagrangian form of dynamics;
Noether's theorem; Hamiltonian dynamics; Poisson brackets.
Prerequisites
An Elementary exposure to the following topics will be sufficient to get started on this unit.
Classical fields; Examples of Classical fields; Eelectromagnetic field as example of fields; Maxwell's equations as field equations.
Relativistic quantum mechanics; Klein Gordon equation; Dirac equation;
Quantum mechanics of a point particle; Time dependent Schrodinger equation.
Different resources are planned to be made available in multiple formats [ audio / video / article style / Slides style etc]
I-1 Overview of Module -1 Classical Fields
The syllabus as in the summary box will be covered in several sub-sessions as indicated below.
The material made available here can be covered in approximately
- 2 to 3 hours of class room lectures and
- 4 hours work of activities outside class room.
The resources are broadly classified as
- Just Talks, with as few equations as possible.
- Chalk Talks will focus on mathematical derivations, proofs etc.
- Activitiy sessions will attempt to cover a broad spectrum of problem solving activity
- Notes and References will establish connections with other topics and areas as well
recommend further study.
I-2 Let's Just Talk with as few equations as possible
I-2.1Talk 1: What is a Classical Fields? Examples
I-2.2 Talk 2: Why reinterpret QM equations as Classical Equations?
I-2.3 Talk 3: How to do classical mechanics of fields?
1-3 Chalk Talks --- Tighten Your Belts
I-3.1 Chalk Talk 1: Functional Derivative
I-3.2 Chalk Talk 2: Action Principle and Euler Lagrange equation of motion
I-3.3 Chalk Talk 3: Hamilton's Equations of Motion and Poisson brackets
I-3.4 Examples: Lagrangian and Hamiltonian for different systems
I-4 Activities For Module-1
I-4.1 WebForm: What is a Classical Field?
I-4.2 WebForm: Classical and Quantum Systems
I-4.3 WebForm: Why Reinterpret QM Equations as Classical Field Equations?
I-4.4 Tutorial: Computing Functional Derivatives
I-4.5 Exercise: Functional Derivative, Lagrangian and Hamiltonian
I-4.6 Exercise: Hamiltonian equations of motion; Poisson brackets
I-5 Notes and References For Module 1
