t3 - updated Thursday 17 th February, 2011 11:41 3. tools...

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Unformatted text preview: updated Thursday 17 th February, 2011 11:41 3. tools for going beyond perturbation theory (a) effective field theory, the renormalization group and running (b) qualitative properties of QCD (c) composite operators and the operator product expansion (d) cutting rules and unitarity + potential between classical charges ( ) + 2 ( ) 2 3 log 1 r ( 1 ) + 2 ( 1 ) 2 3 log 1 r 1 + = ( 2 ) + 2 ( 2 ) 2 3 log 1 r 2 + set r = 1 / 2 ( 2 ) = ( 1 ) + 2 ( 1 ) 2 3 log 2 1 + what are the leading contributions to the ??? + potential between classical charges ( ) + 2 ( ) 2 3 log 1 r ( 1 ) + 2 ( 1 ) 2 3 log 1 r 1 + = ( 2 ) + 2 ( 2 ) 2 3 log 1 r 2 + set r = 1 / 2 ( 2 ) = ( 1 ) + 2 ( 1 ) 2 3 log 2 1 + a confusing sign you might think from the log(1 / ) that ( ) would decrease as increases this combination is NOT ( ) it is a physical quantity that is independent of to this order so when increases, ( ) must increase to keep the combination constant + potential between classical charges ( ) + 2 ( ) 2 3 log 1 r ( 1 ) + 2 ( 1 ) 2 3 log 1 r 1 + = ( 2 ) + 2 ( 2 ) 2 3 log 1 r 2 + set r = 1 / 2 ( 2 ) = ( 1 ) + 2 ( 1 ) 2 3 log 2 1 + what are the leading contributions to the ??? ( 1 ) + 2 ( 1 ) 2 3 log 1 r 1 + a ( 1 ) 2 + b ( 1 ) 3 2 ( log 1 r 1 ) 2 + = ( 2 ) + 2 ( 2 ) 2 3 log 1 r 2 + a ( 2 ) 2 + b ( 2 ) 3 2 ( log 1 r 2 ) 2 + ( 2 ) = ( 1 ) + 2 ( 1 ) 2 3 log 2 1 + = O ( ( 2 ) 2 ( 1 ) 2 ) + O ( ( 1 ) 3 ) ( log 2 1 ) 2 = O ( ( 2 ) + ( 1 ) ) 2 ( 1 ) 2 3 log 2 1 + O ( ( 1 ) 3 ) ( log 2 1 ) 2 accurate so long as ( 1 ) , ( 2 ) , ( 2 ) log 2 1 1 but the relation is much more powerful than that ( 1 ) + 2 ( 1 ) 2 3 log 1 r 1 + a ( 1 ) 2 + b ( 1 ) 3 2 ( log 1 r 1 ) 2 + = ( 2 ) + 2 ( 2 ) 2 3 log 1 r 2 + a ( 2 ) 2 + b ( 2 ) 3 2 ( log 1 r 2 ) 2 + ( 2 ) = ( 1 ) + 2 ( 1 ) 2 3 log 2 1 + = O ( ( 2 ) 2 ( 1 ) 2 ) + O ( ( 1 ) 3 ) ( log 2 1 ) 2 = O ( ( 2 ) + ( 1 ) ) 2 ( 1 ) 2 3 log 2 1 + O ( ( 1 ) 3 ) ( log 2 1 ) 2 accurate so long as ( 1 ) , ( 2 ) , ( 2 ) log 2 1 1 but the relation is much more powerful than that ( 2 ) = ( 1 ) + 2 ( 1 ) 2 3 log 2 1 + O ( ( 2 ) + ( 1 ) ) 2 ( 1 ) 2...
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This note was uploaded on 02/04/2012 for the course PHY 253B taught by Professor Georgi during the Spring '10 term at Princeton.

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t3 - updated Thursday 17 th February, 2011 11:41 3. tools...

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