Dirac algebra

In mathematical physics, the Dirac algebra is the Clifford algebra Cℓ₄(C), which may be thought of as Cℓ_1,3(C). This was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin-½ particles with a matrix representation with the Dirac gamma matrices, which represent the generators of the algebra.

The gamma elements have the defining relation

where ${\displaystyle \eta ^{\mu \nu }\,}$ are the components of the Minkowski metric with signature (+ − − −) and ${\displaystyle {\mathbf {1}}}$ is the identity element of the algebra (the identity matrix in the case of a matrix representation). This allows the definition of a scalar product

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