The Lagrangian for a point particle is just [tex]L=-m\sqrt{1-v^2}.[/tex] If instead we had a continuous distribution of matter, what would its Lagrangian density be? I feel that this should be very easy to figure out, but I can't get a scalar Lagrangian density that reduces to the particle Lagrangian in the appropriate limit.(adsbygoogle = window.adsbygoogle || []).push({});

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# Lagrangian density for continuous distribution of matter

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