- #1
geoduck
- 258
- 2
Is: [tex]\mathcal L=-\frac{m}{2} u^\alpha u_\alpha [/tex]
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]?
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]?