Talk:Crossing (physics)

Unclear Notation
Hi, I just stumbled over those $$q_i$$ explaining the momentum conservation. The text doesn't say what $$q_i$$ actually is. Assuming we're just looking at one vertex (e.g. a photon with momentum $$p$$ interacting with an electron with incoming momentum $$k_i$$ and outgoing momentum $$k'_i$$ (here you could take $$i=1$$)) momentum conservation would require $$p=k_i-k'_i=:q_i$$. In this interpretation $$q_i$$ is the momentum transfer. I admit this is not a complete process since a single vertex is nonsense in the QED regime, but we could have taken $$\phi^3$$-theory.

The other thing I was thinking of is to set $$q_i = k_i$$ bearing in mind to use the right algebraic signs. This would mean to take all external legs of a diagram (apart from $$p$$) and naming their momentum $$q_i$$ or $$k_i$$.

Maybe some of the experts could comment on this? I'm just a poor dumb experimental physicist, so I won't change the article myself ;-) Thank you.  — Preceding unsigned comment added by 80.130.189.9 (talk) 17:15, 19 January 2014 (UTC)

Not a Symmetry
Crossing is not a symmetry, it's an analytic continuation.Likebox (talk) 16:33, 19 October 2008 (UTC)

Just to be clearer--- a symmetry says that something here is equal to something there, for example, the cosh function is even, and that's a symmetry because it says that cosh at x is equal to cosh at -x. Sinh is odd, and that's a symmetry too, because it says that sinh at x is equal to minus sinh at minus x.

An analytic continuation says that the same formula describes two different things. For example, the function exp(x) is not symmetrical, but the values near -100 are the unique analytic continuation of the values near +100.

Crossing is the statement that the same formula for the scattering amplitude will determine the antiparticle scattering by plugging in negative values for the energy. This is a statement of analytic continuation, not symmetry.Likebox (talk) 16:46, 19 October 2008 (UTC)

I might agree that crossing symmetry is not an actual symmetry compared to parity, charge conjugation and time reversal. Still, Peskin and Schroeder refer to it as "crossing symmetry" so maybe we should keep the article name as "crossing symmetry" and explain in the article that the name might be confusing and is rather a historical artifact. --Klappspatier (talk) 18:29, 26 November 2008 (UTC)

I am not sure which is oldest, but there are older (and more appropriate) references like Polkinghorne, "The Analytic S-Matrix" which call it crossing relation. Of course it IS a symmetry in the sense that $$\mathcal{M}( \phi (p) + ... \rightarrow  ...)$$ is symmetric under $$\phi (p) \rightarrow  \bar{\phi} (-p) $$, but "crossing relation" is still more appropriate in my opinion. —Preceding unsigned comment added by 149.217.1.6 (talk) 15:38, 10 March 2011 (UTC)

The beginning of the article explicitly refers to (2-2) scattering processes which is too restrictive. —Preceding unsigned comment added by 149.217.1.6 (talk) 15:42, 10 March 2011 (UTC)