Dirac algebra (contraction gamma matrices)

  • Thread starter IRobot
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  • #1
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I would like to have a general formula, and I am quite sure it must exist, for: [itex]\gamma^{\mu}_{ab}\gamma_{\mu \,\alpha\beta}[/itex] but I didn't succeed at deriving it, or intuiting it, I am troubled by the fact that it must mix dotted and undotted indices.
 

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  • #2
dextercioby
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Why does it have different type of indices ?
 
  • #3
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Because the first gamma matrix is sandwiched between two spinors.
 
  • #4
Bill_K
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IRobot, I think what you are referring to are the Fierz identities, which express the product of two Dirac matrices in terms of matrices in the crossed channel. That is, (γμ)abμ)cd expressed in terms of (γμ)adμ)bc. See here for an exhaustive treatment!
 

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