Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2017

    Am starting Green hyperbolic differential equation from

    • Igor Khavkine, Covariant phase space, constraints, gauge and the Peierls formula, Int. J. Mod. Phys. A, 29, 1430009 (2014) (arXiv:1402.1282)

    So far I have the definition and then the statement of the first remarkable proposition from this article: here.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2017

    added now also the statement of Igor’s lemma 2.5, together with some required infrastructure: here

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 27th 2017
    • (edited Dec 27th 2017)

    I have expanded the statement of the main propositon (here) making explicit the other isomorphism which previously only appeared in an intermediate step in the proof:

    (ker(P)) *Γ Σ,cp(E˜ *)/im cp(P *) (ker(P))^\ast \;\simeq\; \Gamma'_{\Sigma,cp}(\tilde E^\ast)/im_{cp}(P^\ast)

    (For Green hyperbolic differential equations PΦ=0P \Phi = 0.)

    This is the one more frequently used, and I should have highlighted it earlier. This implies for instance that for free field theories with Green-hyperbolic equations of motion PΦ=0P \Phi = 0 , the on-shell polynomial observables are equivalently the off-shell polynomial observables modulo the image of PP, which is used in the construction of the abstract Wick algebra. I have added this to polynomial observables and to microlocal observables. Am working on bringing Wick algebra into shape.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)