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Unformatted text preview: masses? 3. Consider the Higgs potential in the Standard Model: V ( ) = 2 + ( ) 2 (1) with the Higgs feld = + = 1 2 . 1 The potential is SU (2) U (1) invariant. a. (5 pts) In principle one can write SU (2) U (1) quadric invariant of the form V 1 ( ) = 1 ( ~ ) ( ~ ) (2) with ~ the Pauli matrices and 1 a constant. Show that this quadric term can be reduced to that in V ( ) using the Fierz identity 3 X a =1 a 2 ij a 2 kl = 1 2 jk il1 4 ij kl . b. (5 pts) The same as in part a for V 2 ( ) = 1 3 X a,b =1 ( a b ) ( a b ) . (3) 2...
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 Winter '09
 Kovchegov
 Physics, Work

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