How to show gamma matrices are unique?

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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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:

$$\gamma' ~=~ W \, \gamma \, W^{-1}$$

Such new gammas still satisfy the defining Clifford algebra relations.

(Or did I misunderstand your question?)

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

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