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Unformatted text preview: PHY5667 Problem Set #11 (due Tue Nov 9) (1) The gamma five 5 is defined by 5 i 1 2 3 . (i) In the basis of the Dirac spinor and matrices used in class, i.e., = L R , = , show that 5 can be used to project onto the lefthanded or righthanded spinor as P L = L , P R = R , where P L ( 1 5 ) / 2 and P R ( 1 + 5 ) / 2. (ii) Prove the following identities involving 5 , only relying on the relation { , } = 2 1 and the definition 5 i 1 2 3 (that is, do not relay on an explicit form of the gamma matrices): (a) { , 5 } = 0 (b) tr[ 5 ] = 0 . (c) tr[ 5 ] = 0 . (d) tr[ 5 ] = 0 . (e) tr[ 5 ] = 0 . (f) tr[ 5 ] = 4i , where is a totally antisymmetric tensor with 0123 = 1. (g) = 4(  + ) 1 + 4i...
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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.
 Fall '10
 Okui

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