Physics, asked by kunaljain3434, 1 year ago

What restrictions can be placed on the 4 momentum of off-shell particles?

Answers

Answered by uj1

I'm interested in the values that the 4 momenta of off-shell particles are allowed to take.

I suppose if one intends to eventually have these particles interact in a way that generates an on-shell particle, and 3 momentum is conserved at the vertex, then the sum of the 3 momenta of all the off-shell particles must be finite. Can the 3 momentum of an off-shell particle be complex or imaginary?

What about the energy, does this need to be real?

Say on-shell particles have only positive energy values in this system, are the off-shell energy values also restricted to being positive?

Does this relate to the Dirac "spectrum property" that I have seen mentioned?

uj1: An off-shell 4-momentum pp is still a real-valued vector, "off-shell" just means it does not fulfill the correct mass-energy relation for the system it belongs to, i.e. p2=m2p2=m2.

So, no, a 4-momentum cannot be complex, imaginary, or infinite, even off-shell. It's a real-valued 4-vector.

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