Physics 582 Fall 2020 (QFT I)  Lecture on Wednesday October 21, 2020. Today we covered the construction of the ground state and spectrum of a system of fermions at fixed density, introduced a partice-hole transformation and used it to define normal ordered operators relative to the filled Fermi sea. We had a short discussion of the application of this construction to the free Fermi gas. Near the end of the lecture we begun the discussion of the Dirac field theory.