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Detailed Question: A question on quantum field theory. Please let me know if you guys can do it with no mistakes.
1. For identical spin 0 particles in non-relativistic QFT and non-interacting Hamiltonian is:
H = ∫d3xΦ + (x-)(h2/2m ∇2) Φ(x-)
One and two particle states with definite momentum and energy are |K1(1-) = a+(k1) and |k2-,k3-) = a+(k2)a+(k3)|0). The small interaction term is
Hinteraction = ∈∫d3x (Φ+(x-)Φ+. (x-)Φ(x-) + Φ(x-)Φ(x-)Φ+. (x-))
State the dimension of ∈ and calculate the transition matrix element <(k2-, k3-| Hinteraction|k1->
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