HW7_soln

HW7_soln - PHY 5667 Problem Set no. 7 solution Problem 1...

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Unformatted text preview: PHY 5667 Problem Set no. 7 solution Problem 1 The Lagrangian reads L = 1 2 ( )( ) + ( )( ) M 2 2 2 m 2 4 The corresponding Feynman rules are: = i = i a a = i k 2 M 2 + i = 1 (2 ) 3 / 2 2 k = 1 (2 ) 3 / 2 2 k = 1 (2 ) 3 / 2 2 k = 1 (2 ) 3 / 2 2 k a a a a = i k 2 m 2 + i = = k k k k k k k k (i) ( k ) ( k 1 ) ( k 2 ) k k 1 k 2 = ( i )(2 ) 4 ( k k 1 k 2 ) 1 (2 ) 3 / 2 2 k 1 (2 ) 3 / 2 radicalbig 2 k 1 1 (2 ) 3 / 2 radicalbig 2 k 2 = ( i ) 1 (2 ) 1 / 2 2 3 / 2 ( k k 1 k 2 ) 1 / 2 ( k k 1 k 2 ) 1 (ii) ( k 1 ) + ( k 2 ) ( k 1 ) + ( k 2 ) k 1 k 2 k 1 k 2 = ( i )(2 ) 4 ( k 1 + k 2 k 1 k 2 ) 1 (2 ) 3 / 2 radicalbig 2 k 1 1 (2 ) 3 / 2 radicalbig 2 k 2 1 (2 ) 3 / 2 radicalbig 2 k 1 1 (2 ) 3 / 2 radicalbig 2 k 2 k 1 k 2 k 1 k 2 k = k 1 + k 2 = ( i ) 2 (2 ) 4 ( k 1 + k 2 k 1 k 2 ) 1 (2 ) 3 / 2 radicalbig 2 k 1 1 (2 ) 3 / 2 radicalbig 2 k 2 1 (2 ) 3 / 2 radicalbig 2 k 1 1 (2 ) 3 / 2 radicalbig 2 k 2 i ( k 1 + k 2 ) 2 M 2 + i k 1 k 2 k 1 k 2 k = k 1 k 1 = (...
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This note was uploaded on 12/14/2011 for the course PHY 5667 taught by Professor Okui during the Fall '10 term at FSU.

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HW7_soln - PHY 5667 Problem Set no. 7 solution Problem 1...

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