Is: [tex]\mathcal L=-\frac{m}{2} u^\alpha u_\alpha [/tex](adsbygoogle = window.adsbygoogle || []).push({});

a correct Lagrangian for SR (assuming the parameter is proper time rather than world time)?

It leads to the correct EOM when plugged into the Euler-Lagrange equation, [tex]m\frac{du^\alpha}{ds}=0 [/tex]

Or is this the correct Lagrangian:

[tex]\mathcal L=-m \sqrt{u^\alpha u_\alpha} [/tex]

which also leads to the correct EOM, [tex]m\frac{du^\alpha}{ds}=0 [/tex]?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Which Lagrangian is correct for SR?

**Physics Forums | Science Articles, Homework Help, Discussion**