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In the very first chapter of Zee, he talks about the mattress analogy and gives the Lagrangian:

[tex] L=\frac{1}{2} \{ \sum_{a} m \dot{q}^2_{a}-\sum_{a,b} k_{ab}q_{a}q_{b}+...... \}[/tex]

This obviously leads to the equation of motion:

[tex] m \ddot{q_a}=- \sum_{b} k_{ab}q_{b}[/tex]

I don't understand why this is the correct EOM for an oscillator in this 2D set, vibrating purely vertically, surely the restoring force on the a'th oscillator should on depend on it's distance from equilibrium [tex] q_{a} [/tex]. Or perhaps it should depend on things like [tex] q_{a}-q_{b} [/tex], i.e. the total distance between it and the neighbouring particles it is directly connected to.

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# Basic question on Zee-QFT in a nutshell

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