# HW4 - PHY5667 Problem Set#4(due Tue Sep 21(1 To understand...

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Unformatted text preview: PHY5667 Problem Set #4 (due Tue Sep 21) (1) To understand how the conservation of energy and momentum at each vertex in Feynman diagrams arise, let’s look at one of the examples discussed in the lecture, where we had a fermion ψ F and a boson ψ B with an interaction density H int = λ ψ † F ψ F ψ B + λ ∗ ψ † F ψ F ψ † B . In the lecture, we showed that the amplitude for the scattering process F( vector k 1 )+F( vector k 2 ) → F( vector k ′ 1 )+F( vector k ′ 2 ) is given by Amp. = ( | a F ( vector k ′ 2 ) a F ( vector k ′ 1 ) × × ˆ T braceleftbigg 1 2! · 2 · integraldisplay d t d 3 vectorx ( − i λ ) ψ † F ψ F ψ B ( t,vectorx ) integraldisplay d t ′ d 3 vectorx ′ ( − i λ ∗ ) ψ † F ψ F ψ † B ( t ′ ,vectorx ′ ) bracerightbigg × × a † F ( vector k 1 ) a † F ( vector k 2 ) | ) = ( − i λ )( − i λ ∗ ) integraldisplay d t d 3 vectorx d t ′ d 3 vectorx ′ parenleftbigg a F2 ′ ψ † F a F1 ′ ψ † F ′ ψ B ψ †...
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