Dirac algebra

In mathematical physics, the Dirac algebra is the Clifford algebra Cℓ4(C), which may be thought of as Cℓ1,3(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. σ μ ν = 1 4 [ γ μ , γ ν ] , {displaystyle sigma ^{mu u }={frac {1}{4}}left,}     (I4) [ σ μ ν , σ ρ τ ] = ( − η τ μ σ ρ ν + η ν τ σ μ ρ − η ρ μ σ τ ν + η ν ρ σ μ τ ) , {displaystyle left=left(-eta ^{ au mu }sigma ^{ ho u }+eta ^{ u au }sigma ^{mu ho }-eta ^{ ho mu }sigma ^{ au u }+eta ^{ u ho }sigma ^{mu au } ight),}     (I5)Multiplying the Dirac equation by its conjugate equation yields: In mathematical physics, the Dirac algebra is the Clifford algebra Cℓ4(C), which may be thought of as Cℓ1,3(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.