W02L05_Dirac Algibra

Use the identity to commute a thru to the right side

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Unformatted text preview: a × b ) ⋅ σ + a ⋅ b 12 + i(b × a ) ⋅ σ = 2 a ⋅ b 12 c) Use this to obtain an expansion for Tr (abcd ) in terms of dot products using the result of (b). (use the identity to commute a thru to the right side using (b) and then bring it back to the front). Tr (abcd ) = 2 a ⋅ b Tr (cd ) − Tr (bacd ) ( )( ) = 4 (a ⋅ b )(c ⋅ d ) − 2(a ⋅ c)Tr (bd ) + Tr (bcad ) = 4 (a ⋅ b )(c ⋅ d ) − 4 (a ⋅ c)(b ⋅ d ) + 2(a ⋅ d )Tr (bc) − Tr (bcda )...
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