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- They form a complete set of commuting operators for the Dirac algebra.
- For details, see bispinor and Dirac algebra.
- The specific Clifford algebra employed in the Dirac equation is known today as the Dirac algebra.
- For the higher order elements of the Clifford algebra in general, and their transformation rules, see the article Dirac algebra.
- This representation, which is detailed in the article on the Dirac algebra, acts in the passive sense on the themselves.
- They extended this approach further to relativistic phase space by applying the phase space interpretation of Mario Sch�nberg to the Dirac algebra.
- For a full description of the remaining basis elements other than and of the Clifford algebra, please see the article Dirac algebra.
- The Dirac algebra and the Duffin Kemmer Petiau algebra appear as special cases of the parafermionic algebra for order p = 1 and p = 2, respectively.
- However, in contemporary practice, the Dirac algebra rather than the space time algebra continues to be the standard environment the spinors of the Dirac equation " live " in.
- Consequently, we can make a projection operator from it that projects out the sub-algebra of the Dirac algebra that has spin oriented in the ( a, b, c ) direction: