Why does the following Lagrangian not have the correct non-relativistic limit? It is correct except for the derivative of proper time with respect time. But that factor goes to 1 so why is the expression wrong?(adsbygoogle = window.adsbygoogle || []).push({});

## L = -(\frac{1}{2}mu^{\mu}u_{\mu} + qu^{\mu}A_{\mu})\frac{d\tau}{dt} ##

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# I Non-relativistic limit of the Lagrangian

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