How to show gamma matrices are unique?

[kof9595995]

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?

 

[strangerep]

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:

<br /> \gamma&#039; ~=~ W \, \gamma \, W^{-1}<br />

Such new gammas still satisfy the defining Clifford algebra relations.

(Or did I misunderstand your question?)

 

[kof9595995]

I mean, given a basis, gamma matrices must be unique, aren't they?

 

[strangerep]

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... :-)

 

[kof9595995]

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.