- #1

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## Main Question or Discussion Point

I've seen that the lagrangian for a relativistic free particle is

[tex] -mc \sqrt{\eta_{\mu\nu} \dot{x^{\mu}}{\dot{x\nu}} [/tex] but when I construct the hamiltonian as

[tex] p_{\mu} \dot{x^{\mu}} - L [/tex]

I seem to get zero. Im not really sure what I'm doing wrong. I find that if in the first term of the hamiltonian, I only sum over spatial indices, I end up with γmc^2 which is what I would expect.

[tex] -mc \sqrt{\eta_{\mu\nu} \dot{x^{\mu}}{\dot{x\nu}} [/tex] but when I construct the hamiltonian as

[tex] p_{\mu} \dot{x^{\mu}} - L [/tex]

I seem to get zero. Im not really sure what I'm doing wrong. I find that if in the first term of the hamiltonian, I only sum over spatial indices, I end up with γmc^2 which is what I would expect.