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Golden Rule for Decays in Griffiths' Introduction to Elementary Particles ?

  1. Mar 18, 2010 #1
    Golden Rule for Decays in Griffiths' "Introduction to Elementary Particles"?

    Hello, I'm getting a bit bogged down in constant factors while reading Griffiths' "Introduction to Elementary Particles", 1st edition. In particular, I'm having problems with equation 6.15:
    d\Gamma = |M|^{2}\frac{S}{2\hbar m_{1}}\left[
    \left(\frac{c\, d^{3}p_{2}}{(2\pi)^{3}2E_{2}}\right)
    \left(\frac{c\, d^{3}p_{3}}{(2\pi)^{3}2E_{3}}\right)\cdots
    \left(\frac{c\, d^{3}p_{n}}{(2\pi)^{3}2E_{n}}\right)\right]\times

    I've found some slides online at http://www-pnp.physics.ox.ac.uk/~libby/Teaching/Lecture4.pdf that discuss normalizing the wave function and phase space so it is Lorentz invariant, but this only explains part of my problem. What I still don't understand is:
    • Where do the [tex]c[/tex] in the numerators of the momentum terms come from?
    • Where does the [tex](2\pi)^{4}[/tex] term before the delta function come from?
    • Where did the [tex]\hbar^{3n}[/tex] in the density of states go? (The [tex]\frac{1}{(2\pi\hbar)^{3n}}[/tex] is responsible for the [tex]2\pi[/tex] factors in the momentum terms, right?)
    • Why doesn't the first fraction have [tex]m_{1}c^{2}[/tex] in the denominator?

    Any assistance would be greatly appreciated.
  2. jcsd
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