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### Syllabus

Examples of classical Fields; Functional derivative; Lagrangian and Lagarangian
density; Action principle; Euler Lagrange equations of motion; Canonical
momentum; Hamiltonian; Poisson bracket.

### Prerequisites

Lagarangian and Hamitonian formulations of dynamics of point particles.

### Instruction Goals

To explain the following:

• What is meant by a picture (of time evolution)in quantum theory?
• Definition and examples of calculation of functional derivatives
• Using variantional principle to derive Euler Lagrange equations of motion.
• Setting up the Hamiltonian

### Lessons

1. Examples of classical fields
2. Functional derivative
3. Action Fucntional
4. Hamiltonian formulation of classical fields

### Suggested Questions and Problems

1. Computing functional derivative.
2. Deriving Euler Lagrange equations of motion from Lagrangian density
3. Computing Haimltonian

### Where do we need all, or some part, of this unit

The steps to quantize  a classical field require the contents of this unit.
Most of the cases the field equation is given, or is known. One needs to find
the Lagrangian density, compute the  momenta canonically congjugate to the
fields. The act of quantization consists in assuming the commutation relation
between a field operator and its canonical momenta to be given by $$ihbar$$
times the Poisson bracket.

### What is not included here but will in come later units?

Symmetries and conservation laws. Construction of generators of symmetry
transformations; Lorentz transformations and Poincare group. Energy momentum
and angular momentum tensors for Schrodinger, Klein Gordon and Dirac fields.

### Planned for Next Phase

To draw flow charts, concept maps.

### Notes and References

1. David Lurie, {\it Particles and Fields}, Interscience Publishers (1968)
2. L. I. Schiff, {\it Quantum Mechanics}, McGraw Hill Publishing Co. New York (1949)
3. M.E. Peshkin and David V. Schroeder, {\it An introduction to Quantum Field Theory}, Levant Books Kolkata (2005)

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