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Unformatted text preview: commute with the Dirac Hamiltonian, so S r is also not conserved! In particular, ) ( ] , [ op op op p c i S H r r h r × + = . Proof: We see that x op y z z y x z x z y x y x x x x z z y y x x x x op p c i p p c i S mc p S c p S c p S c S mc p p p c S mc p c S H ) ( ) ( ] , [ ] , [ ] , [ ] , [ ] , ) ( [ ] , [ ] , [ 2 2 2 r r h h r r × = − = + + + = + + + = + ⋅ = where I used the fact that ] , [ ] , [ = = x x x S S , z x y i S h − = ] , [ , and y x z i S h = ] , [ . The other components are done similarly....
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.
 Spring '07
 FIELDS
 mechanics, Angular Momentum, Momentum

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