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Unformatted text preview: a. (5 pts) Show that 1 ( ) =1 2 2 + 3 2 2 + analytic terms in . b. (10 pts) Dene the parameter by 2 = 2 c exp  Z d ( ) with and c some constants. Show that one can choose and c such that ln 2 2 = 1 2 + 3 2 2 ln( 2 ) + o ( ) . (1) c. (10 pts) Solve Eq. (1) above for the running coupling ( 2 ) in terms of ln( 2 / 2 ) assuming that ln( 2 / 2 ) 1 and keeping all terms which decrease with increasing 2 less rapidly than ln3 ( 2 / 2 ). d. (10 pts) Show that 2 = 2 e1 2 ( 2 ) 3 / 2 2 [1 + o ( )] (2) and prove that this 2 is independent. 1...
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This note was uploaded on 07/28/2011 for the course PHYSICS 880.02 taught by Professor Kovchegov during the Winter '09 term at Ohio State.
 Winter '09
 Kovchegov
 Physics, Mass, Work

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