Please help; calculation phase space -> how do I use the Delta functions?

[marlon1]

Can somebody help me out? I'm reading about formulas for cross sections for spin1 particles but I don't understand the delta functions, in calculating the 2particle pahse space psi

For example the interaction; A+B -> C+D has the formula;

psi= (2pi)^2 delta(Pa+Pb-Pc-Pd) d3Pc d3Pd / 4EcEd

then all the books say the same;

delta(Pa+Pb-Pc-Pd) d3Pd = delta (Ea+Eb-Ec-Ed)


can somebody explain this to me?

the left side delta is zero everywhere pa+pb =not pc+pd.

the integral over the delta function d3Pd is;
1 for pd<pa+pb-pc and
0 for pd>pa+pb-pc

? how do I use this?

 

[marlon1]

Vergeet niet dat de je p3's en p4's hebt! (p4=(E,p)

\delta^{4}(p1+p2-p3-p4) d^{3}p4
=\delta(E1+E2-E3-E4) <br /> \delta^{3}(p1+p2-p3-p4)d^{3}p4
=\delta(E1+E2-E3-E4) \delta^{3}(-p3-p4) d^{3}p4 (CM frame: p1=-p2)
=\delta(E1+E2-E3-E4) \delta(x) dx (x= -p3-p4 = 0 CM frame)
= \delta(E1+E2-E3-E4) * 1 = \delta(E1+E2-E3-E4)
QED