Chapter IV Gauge Field Lecture 2 Books Recommended: Lectures on Quantum Field Theory by Ashok Das Advanced Quantum Mechanics by Schwabl

Lagrangian Density ------(1) Where From (1) ------(2)

Also, ------(3) Thus, Eq, of motion will be ------(4) Momentum conjugate to field ----(5)

From (5), we get ----(6) And --------(7) It is not possible to apply canonical quantization to all four components of radiation field.

Exercise: Another Lagrangian density for E.M. Field is --------(8) Derive Eq of motion from above Show that Eq (1) and (8) are differ by total divergence

Free Electromagnetic field and quantization For free field ---(9) Sol of Poisson Eq will be = 0 ----(10)

For E.M field we have ---(11) Lagrangian density for free field ---(12) Here we used

Hamiltonian density for free e.m. Field --- --- --------(13)