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ps09 - Physics 651 Problem Set 9 Read Chapter 4 1 Prove...

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Physics 651 – Problem Set 9 (due 11/10/03) Read Chapter 4. 1. Prove Wick’s theorem T { φ ( x 1 ) φ ( x 2 ) . . . φ ( x n ) } = : φ ( x 1 ) φ ( x 2 ) . . . φ ( x n ) : + : all possible contractions : by induction on n . 2. Show that the contraction of Dirac fields ψ a ( x ) ¯ ψ b ( y ) = { ψ + a ( x ) , ¯ ψ - b ( y ) } ; for x 0 > y 0 , -{ ¯ ψ + b ( y ) , ψ - a ( x ) } ; for x 0 < y 0 , is equal to the fermion propagator [ S F ( x - y )] ab . Also show that the contractions
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