Weinberg in his 1st book on QFT writes in the paragraph containing 2.5.12 that we may choose the states with standard momentum to be orthonormal. Isn't that just true because the states with any momentum are chosen to be orthonormal by the usual orthonormalization process of quantum mechanics? Similarly, doesn't 2.5.13 come directly from the unitarity of the operators U? What is Weinberg trying to say? Then later when he considers inner product relations between arbitrary momenta, then if p and p' are in the same class, then they would have same k. So, if one defines a k', that might not be a standard momentum. So, is Weinberg also allowing for non-standard momenta? But then he considers N(L^-1(p)p')=1 while writing the second equation between 2.5.13 and 2.5.14. This strongly suggests he is only taking standard momenta. Moreover, if I vary p' even in the different class, according to his definition k' is varying. But k' is a fixed standard momentum in a class. I again don't get what is going on. Plus, I don't get anything he says between 2.5.14 and 2.5.17 (excluding 2.5.14 and 2.5.17). Can somebody explain what he is trying to say? That would be great.