In the representation theory of Lorentz transformations, the words Clifford algebra and Dirac algebra are used interchangeably. However, there is a distinction between the two. Indeed, the Dirac algebra is the particular Clifford algebra ##Cl_{4}({\bf{C}})\equiv Cl_{1,3}({\bf{C}})## with a basis generated by the matrices ##\gamma^{\mu}## called Dirac matrices which have the property that ##\{\gamma^{\mu},\gamma^{\nu}\}=2g^{\mu\nu}##.(adsbygoogle = window.adsbygoogle || []).push({});

On the other hand, the spinor representation of the Lorentz algebra can be obtained using the Dirac matrices which obey the Dirac algebra.

The above is a qualitative picture of the key difference between the Clifford algebra, Dirac algebra and the Lorentz algebra.

Can someone please flesh out the mathematical details?

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# A Algebra - Clifford, Dirac, Lorentz

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