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Why the gamma matrices are taken 2 by 2 (Pauli matrices) in 3 dimensional Clifford Algebra. As in 4D Clifford Algebra the matrices are 4 by 4, in 3D Algebra why are they not 3 by 3 matrices? The question can be asked another way that should we use the representation according to the components of Dirac spinor?

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  • $\begingroup$ How do you know such a representation does not exist? A clifford algebra describes any objects that obey the laws of the algebra--whether they're matrices or some other mathematical objects with some product operation. $\endgroup$ – Muphrid Jan 14 '17 at 5:39
  • $\begingroup$ I understand your argument. I am studying Dirac equation in 2+1 D, I think the reason to take gamma matrices 2 by 2 in my case is that the Dirac spinor is two component here. I want to know that if there is any other reason also? $\endgroup$ – Zohaib Aarfi Jan 14 '17 at 5:44
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/53318/2451 , physics.stackexchange.com/q/259514/2451 , physics.stackexchange.com/q/41282/2451 and links therein. $\endgroup$ – Qmechanic Jan 14 '17 at 5:48
  • $\begingroup$ #Qmechanic it was helpful, thanx. $\endgroup$ – Zohaib Aarfi Jan 14 '17 at 5:59