ps09soln

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

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online