- #1
MManuel Abad
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Hi there, physics lovers. I'm studying field theory. So far, so well. I got it with the lagrangian density. I understood it. But then I DIDN'T FIND stuff about the Hamiltonian density. I couldn't find anything in Landau-Lifgarbagez series, and that makes me worry. I've been looking in the internet and I couldn't find ANYTHING about it. I found some stuff in the Goldstein, but not as explained and as extended as I'd like. Besides, I found in the Goldstein what could be considered the equivalent canonical equations for this Hamiltonian density, but in some other reference (which I don't remember) I found these equations very very different. That is kind of driving me crazy. Could you please help and tell me:
- What is the Hamiltonian density?
- How can I derive the Canonical field equations and what are they? (if there's such a thing, as there is in particle mechanics)
- Adventages and disadventages of the Hamiltonian density formulation?
- Why not many people use it? I mean, through the internet I found stuff about Klein-Gordon fiels and that. They find the lagrangian density, they use the lagrangian field equations and find the equations for the field. Then they find the Hamiltonian density... and that's all. ¿Why don't they use the hamiltonian field equations (again, if there's such a thing) for finding the equations of motion?
Please, I'm kind of desperate. This is not homework (I'm just in the fourth semester), it's something I'm studying on my own.
Greetings.
- What is the Hamiltonian density?
- How can I derive the Canonical field equations and what are they? (if there's such a thing, as there is in particle mechanics)
- Adventages and disadventages of the Hamiltonian density formulation?
- Why not many people use it? I mean, through the internet I found stuff about Klein-Gordon fiels and that. They find the lagrangian density, they use the lagrangian field equations and find the equations for the field. Then they find the Hamiltonian density... and that's all. ¿Why don't they use the hamiltonian field equations (again, if there's such a thing) for finding the equations of motion?
Please, I'm kind of desperate. This is not homework (I'm just in the fourth semester), it's something I'm studying on my own.
Greetings.
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