Some Remarks on Fields

• fields as stupid book-keeping tool? Cf. Feynman's Nobel Prize speech. Do you really understand what a field is?
• but there is modern point of view: EM as U(1) gauge theory. Automatically brings in the concept of a field. Or can one do gauge theories without fields.
• retardation is a key point: if retardation is neglected: Breit-formula (Landau-Lifshitz Vol. IV) as $c\to \infty$ limit.
• QED Lagrange density just contains minimal coupling to vector potential, no explicit interaction between particles. Coulombs law follows as first term in an expansion in $1/c$, cf. (Landau-Lifshitz Vol. IV).