ps09soln - PHYS651 Problem Set 9 Solutions 1 This is pretty...

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Unformatted text preview: PHYS651: Problem Set 9 Solutions 1 . This is pretty well done in P.S. at page 90 2 . Using the definitions of ψ ± and ¯ ψ ± we find: { ψ + a ( x ) , ¯ ψ- b ( y ) } = Z d 3 ~ p (2 π ) 3 1 p E ~ p e- ip · x X s u s a ( p ) × Z d 3 ~ k (2 π ) 3 1 p E ~ k e- ik · y X r ¯ u r b ( p ) { a s ~ p , a r † ~ k } = Z d 3 ~ p (2 π ) 3 1 E ~ p e- ip · ( x- y ) X s ( u s ( p )¯ u s ( p )) ab = Z d 3 ~ p (2 π ) 3 1 E ~ p e- ip · ( x- y ) ( p/ + m ) ab Which we recognized (equation 3.114) as < | ψ a ( x ) ¯ ψ b ( y ) | > . The same way we find that:-{ ¯ ψ + b ( y ) , ψ- a ( x ) } =- < | ¯ ψ b ( y ) , ψ a ( x ) | > Hence ψ a ( x ) ¯ ψ b ( y ) | {z } = < | T { ψ a ( x ) ¯ ψ b ( y ) | > = [ S F ( x- y )] ab Where my underbrace means contraction. 3 . P.S. page 121,122 4 . P.S. page 125. 5 . To lowest order in μ the feynmann diagram contributing to the Φ decay is: u p p P This comes from the interacting part of the hamiltonian which is: H I ( t ) = μ 2 Z d 3 x Φ( x ) φ ( x ) φ ( x ) To lowest order the T matrix is very simple: iT Φ → φφ =- iμ (2 π...
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This note was uploaded on 09/28/2008 for the course PHYS 651 taught by Professor Tye,henry during the Fall '03 term at Cornell.

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ps09soln - PHYS651 Problem Set 9 Solutions 1 This is pretty...

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