Dirac equation & Dirac matrices

[eoghan]

Hi! I was taught that the dirac matrices are AT LEAST 4x4 matrices, so that means that I can find also matrices of higher dimensions. The question is: what do these higher-dimension-matrices represent? Are they just mathematical stuff or have they got a physical meaning? I ask that because in every textbook and in every course I used only the 4x4 matrices...
Thanks

 

[IcedEcliptic]

Hi! I was taught that the dirac matrices are AT LEAST 4x4 matrices, so that means that I can find also matrices of higher dimensions. The question is: what do these higher-dimension-matrices represent? Are they just mathematical stuff or have they got a physical meaning? I ask that because in every textbook and in every course I used only the 4x4 matrices...
Thanks

You can represent a matrix of any complexity you wish, but only experimentation can show if there is something physical about it. A string theorist might have an 11X11 matrix, but that does not prove 11 dimensions in reality I think. I don't know for sure, and I am new. I hope this is not presumptuous.