Confusion (1) from Weinberg's QFT.(unitary representation)

[kof9595995]

This describes ortho_normality_. Orthogonality is the waker statement assuming p and p' being different and concluding that the inner product vanishes - this is independent of the scaling of the metric. But for orthonormality, the precise factor matters, and different factors define different concepts of orthonormality.

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Ok, that's more or less satisfactory to me, thanks.

 

[kof9595995]

You keep coming back to this, but this is a result about inner product spaces, and we're not dealing with an inner product space.

Unfortunately I don't know rigged Hilbert spaces well enough to explain what you should be saying instead, at least not without making a bigger effort than I have time for right now.

Sorry about that. What you said makes sense, but some other people don't seem to insist that this is the crux of the problem, and I have to mention it to make my point sometimes.

 

[Fredrik]

If what I said is the crux of the problem or not depends on if we're trying to explain why your original argument doesn't work, or how things work in the space we're actually dealing with. I've been focusing on the former. Someone who focuses on the latter will of course emphasize other things. I don't think any of them disagrees with me about what's wrong with the argument.