National Seminar on Theoretical Physics, 14-15 Sep, 2023.
Venue: Department of Physics, Government Brennen College, Dharmadam, Thalassery, Kerala.
Sponsored by Department of Collegiate Education, Govt. of Kerala.
Introduction to fields and their quantization
Topics: Classical fields model systems with infinitely many degrees of freedom. Examples of field equations. Approaches to the quantum theory. Lagrangian, Hamiltonian and action for fields. Euler-Lagrange equations and Hamilton's equations. Nonlinear Schrodinger field in 1+1 dimensions. Classical nonlinear Schrodinger equation and conserved quantities. Hamiltonian-Poisson bracket and Lagrangian formulations of NLSE. Noether's Theorem and conserved quantities. Canonical quantization. Canonical commutation relations. Number and Hamiltonian operators. Raising and lowering operators, vacuum state. N-particle wave function and its normalization. Physical interpretation: system of N bosons with contact interactions.
Some brief lecture notes are here.
A set of problems is here.