Talk:Hamiltonian field theory
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 | The contents of the Covariant Hamiltonian field theory page were merged into Hamiltonian field theory on 24 October 2017. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
Should have been it's own article long ago[edit]
The analytical mechanics and especially classical field theory articles on WP are currently a mess. Anything similar (e.g. Lagrangians for systems of particles and Lagrangian densities for fields) are mushed into each other within the same articles. Things would be much easier to follow if there were separate articles on general analytical mechanics, general classical field theory, Lagrangian mechanics, Lagrangian field theory, Hamiltonian mechanics, and Hamiltonian field theory. The first two are separate but each article needs work. The rest do not have clean cut articles (I'll check their talk pages in detail later).
So, I started this article, as it was a redlink and thre doesn't seem to be anywhere where Hamiltonian field theory is plainly described. I know the equations are written clumsily using nabla and time partial derivatives instead of compact tensor index notation, and the text is very pedantic, but I want to be absolutely clear which derivatives are used. Most of the literature is not clear about overdots for partial time derivatives, and we should avoid abuses of notation. Both of these are in footnotes.
Much more to follow. M∧Ŝc2ħεИτlk 14:44, 31 July 2015 (UTC)
To do list, or scrap the article[edit]
Plenty of things for this article:
- Priority
- Field theoretic Piosson brackets,
- Phase space of fields
- Derivation from principle of least action, and/or Lagrangian field equations
- Examples (Newtonian gravitational field? Classical EM field? Nonlinear fields? others...)
- Relativistic covariant generalization (we could merge covariant Hamiltonian field theory into this article)
- Other useful bits
- Continuity equation in terms of the Hamiltonian
- Relation to the stress-energy tensor?
If anyone can find an article or articles which already has all these things in one place, then in principle this article should be scrapped. If the above content is scattered here, there, everywhere (which seems more likely) they should be merged into this article. M∧Ŝc2ħεИτlk 15:38, 31 July 2015 (UTC)