How to show gamma matrices are unique?

  • Thread starter kof9595995
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  • #1
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Main Question or Discussion Point

In most of the physics textbooks I read they only give one or two representations of gamma matrices, but none gives a proof, so how can I prove it from the Clifford algebra?
 

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  • #2
strangerep
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In most of the physics textbooks I read they only give one or two representations of gamma matrices, but none gives a proof, so how can I prove it from the Clifford algebra?
??? The form of gamma matrices is not unique in general.
Consider similarity transformations like:

[tex]
\gamma' ~=~ W \, \gamma \, W^{-1}
[/tex]

Such new gammas still satisfy the defining Clifford algebra relations.

(Or did I misunderstand your question?)
 
  • #3
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I mean, given a basis, gamma matrices must be unique, aren't they?
 
  • #4
strangerep
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I mean, given a basis, gamma matrices must be unique, aren't they?
Er, what precisely do you mean by "basis" in this context?

(I'm still having trouble understanding what point is bugging you... :-)
 
  • #5
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Maybe I should rephrase it: Any two sets of matrices satisfying Clifford algebra, can be linked by a similar transformation.
I think this should be a quite famous theorem, but I don't know where to find it.
 

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