- #1
fa2209
- 23
- 0
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. I am 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. I am 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.