Normalization of $\langle p_1 p_2 \vert p\rangle$ in RelQM and NonRelQM Suppose a particle p of three momentum $\vec p$ decays into two particles of 3-momentum $\vec p_1$ and $\vec p_2$. I know the question might sound stupid but right now my brain is full stop: 
Is the following "ok" $$\langle \vec p_1, \vec p_2 \vert \vec p\rangle = (2\pi)^3 \delta^3(\vec p-\vec p_1-\vec p_2)?$$ If one wants a Lorentz invariant normalization one should use (see eg Srednicki 2011, eq. 9.3) now four vectors!
$$\langle p_1 p_2 \vert p\rangle = 2p_0 (2\pi)^3 \delta^3(\vec p-\vec p_1-\vec p_2)$$ but my question then is how this translates to nonrelativistic physics/normalizations? Or perhaps there can't be a nonrelativistic limit of this because in ordinary quantum mechanics particle number is fixed?
 A: Well firstly, you're trying to put two concepts together that do not usually go.
Lorentz invariance is a special property of relativistic quantum mechanics. You do not have Lorentz invariance in non-relativistic Quantum Mechanics. 
As regards your first expression, I do not think that this is correct. For one, it would give an infinite amplitude on-shell, that is, at
$$ \vec{p} = \vec{p_1} + \vec{p_2} $$
Also, the idea of particle decay in non-relativistic Quantum Mechanics is not defined. The particle number must stay constant. You need (relativistic) Quantum Field Theory to properly describe particle decay and variable particle number (creation and annihilation etc.)
That is, you need to do a full QFT calculation to get find the amplitude for particle decay. I'm sure this will be covered in Srednicki. Personally I prefer Peskin & Schroeder. Or even better if you want to have an overview of the calculation without too much formulaity is Griffiths' Introduation to Elementary Particles, Ch. 6. 
Finally, yes indeed, to get a Lorentz invariant quantum field state $\vert p \rangle $ you need the factor of $2 E_{\vec{p}}$. This is purely a convention though, you do not need to include this factor in your normalisation if you don't want to, or if you wanted to normalise relative to some other state say. The cost of this would be loosing Lorentz invariance. Again, see Peskin & Schroeder pg. 22-23 for a short derivation.
So to sumarise, it does not translate to non-rel. QM.
