LSZ reduction, momentum diagram, QFT

I was initially confused about which way to choose the sign of the momentum, since it gives rise to different exponential momentum combinations and thus different deltas for momentum conservation. I came to the conclusion that it doesn’t matter as long as you are consistent, which I found to be correct when I came across Sign ambiguity when going from position to momentum space evaluating Feynman diagrams.

My question pretty much is about the definition of consistency here. There are two things to consider:

1. having some consistent pattern to decide which external vertices you point toward a vertex, and which away from a vertex

2. what system you choose to denote positive and negative relative to, i.e right and left, up and down, or into a vertex and out of a vertex.

My choice I like to use is: 1. all point in the same direction - e.g. right 2. + or - given by whether in to a vertex or out

Are the choices 1) and 2) which I talk about sufficient to obtain consistency? Is it even correct to referring to what you may denote by plus or minus using left / right or should it always be into and out of a vertex?

Regarding number 1, I feel as though the easier option is to label everything in same direction, but say I am considering variations of a diagram by keeping the external points fixed (1,2,3,4). I believe another way of consistency would be to always associate the same direction with the same external point - these could be all the same, three same, one not, two-two - it does not matter. Am I correct in thinking this is a valid move?

• Hi, I edited your post rather heavily, but I still can't quite tell what "the momentum" in your first sentence refers to. Are you talking about momentum vectors in the Feynman diagram? What do you mean by "right and left" for such a diagram, given that the diagram really are just graphs and have no axes? May 10, 2019 at 16:39