Physics 583 (QFT II) Spring 2021 Zoom lecture on Tuesday February 2, 2021. Today we discussed the non-linear sigma model as the low energy limit of a scalar field theory with a spontaneously broken symmetry and derived the effective Lagrangian. We also discussed Schwinger-Dyson equations for a complex scalar field with global U(1) symmetry and for QED, and derived the QED Ward Identity. In the second half of the lecture we introduced the loop expansion and derived the generating functional of the 1PI irreducible vertex functions for 𝜙^4 theory at the tree level.