Chapter4_23 - PHY4604 R. D. Field Generators of the Group...

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PHY4604 R. D. Field Department of Physics Chapter4_23.doc University of Florida Generators of the Group O(3) Proof: Starting with the series expansions L + + + = = = 2 ! 2 1 1 ! 1 1 A A A e n n n A L + = 5 ! 5 1 3 ! 3 1 sin x x x x L + = 4 ! 4 1 2 ! 2 1 1 cos x x x we see that = + + + + = + + + + = = 1 0 0 0 ) cos( ) sin( 0 ) sin( ) cos( 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 ) ( 3 ! 3 1 3 ! 3 1 2 ! 2 1 2 ! 2 1 3 3 ! 3 1 2 2 ! 2 1 z z z z z z z z z z z z z z z z z I z z I I I e R z z φ L L Arbitrary Rotation the 3-Space: The three generators of arbitrary rotations in 3-space are = 0 1 0 1 0 0 0 0 0 x I = 0 0 1 0 0 0 1 0 0 y I = 0 0 0 0 0 1 0 1 0 z I Note that
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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.

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