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• 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:

$(ker(P))^\ast \;\simeq\; \Gamma'_{\Sigma,cp}(\tilde E^\ast)/im_{cp}(P^\ast)$

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

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 $P \Phi = 0$ , the on-shell polynomial observables are equivalently the off-shell polynomial observables modulo the image of $P$, 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.