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Energy-momentum Four-vectors

  1. Oct 22, 2005 #1
    Does anyone know how you find the length of the energy-momentum four-vector for a system of particles?
    where length is:

    Do you first add the corresponding vector elements then find the length
    find the length of each particle first then sum the individual lengths.

  2. jcsd
  3. Oct 22, 2005 #2
    Both values will give you invariants, although the energy-momentum four-vector ([itex]p^\mu[/itex]) of the whole system is equal to the sum of all the individual [itex]p^\mu[/itex], and therefore the length of [itex]p^\mu[/itex] for the system is the length of the sum of all the individual [itex]p^\mu[/itex].
  4. Oct 22, 2005 #3


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    Staff: Mentor

    It's exactly analogous to finding the magnitude of the total three-momentum of a system of particles. In that case, you find the total x-momentum, total y-momentum, and total z-momentum of momentum, then use them to find the magnitude of the total-momentum vector.
  5. Oct 22, 2005 #4
    If the particles are interacting through when they are seperated (e.g. two charged particles) then the addition of the two 4-vectors is meaningless. Only systems of non-interacting particles anmd systems of particles which interact only through contact forces can be added in a meaningful way. To add the vectors you add components and then take find the magnitude.

    This web page I created will get into great detail regarding this. See

  6. Oct 23, 2005 #5
    Is this method ok?

    Thanks for the clarification...

    What I was trying to do was find the lengths of the four-vectors of this reaction before and after.
    p + p ==> p + p + Z

    Where a proton with 300GeV hits a stationary proton, then producing a particle Z.

    I calculated the length of the Four-vector before the reaction in the stationary proton's frame.

    I then equate this to the length of the four-vector after the collision in the
    center-of-mass frame to extract the rest mass of the Z particle.


    Question, is there anything wrong with my method?

    I have assumed that after the collision the two protons and the Z particle are at rest, since I want the maximum possible rest mass of Z. Momentum in the COM from is zero so it should be ok?

  7. Oct 24, 2005 #6


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    Staff: Mentor

    Yes, that's a reasonable way to proceed. What you end up with is the largest mass the Z can have, and still be produced under these initial conditions.
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