From Eduardo Fradkin
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Physics 582 Fall 2020 lecture on 8/31/2020. We continued the discussion of classical field theory. In this lecture we discussed the requirements of locality and Lorentz invariance on the form of the classical action for scalar fields. We used the least action principle to derive the classical equations of motion for the scalar field and derived the classical Hamiltonian. We discussed the free massive scalar field and showed that the Klein-Gordon equation is the classical equation of motion. We showed that the theory does not have negative energy states but positive an negative frequency components of its plane wave solutions. We also discussed the canonical formalism.