ガンマ行列
ガンマ行列の縮約については、以下が成り立つ。
γ μ γ μ = d {\displaystyle \gamma ^{\mu }\gamma _{\mu }=d}
γ μ γ ν γ μ = ( 2 − d ) γ ν {\displaystyle \gamma ^{\mu }\gamma ^{\nu }\gamma _{\mu }=(2-d)\gamma ^{\nu }}
γ μ γ ν γ ρ γ μ = 4 g ν ρ − ( 4 − d ) γ ν γ ρ {\displaystyle \gamma ^{\mu }\gamma ^{\nu }\gamma ^{\rho }\gamma _{\mu }=4g^{\nu \rho }-(4-d)\gamma ^{\nu }\gamma ^{\rho }}
γ μ γ ν γ ρ γ σ γ μ = − 2 γ σ γ ρ γ ν + ( 4 − d ) γ ν γ ρ γ σ {\displaystyle \gamma ^{\mu }\gamma ^{\nu }\gamma ^{\rho }\gamma ^{\sigma }\gamma _{\mu }=-2\gamma ^{\sigma }\gamma ^{\rho }\gamma ^{\nu }+(4-d)\gamma ^{\nu }\gamma ^{\rho }\gamma ^{\sigma }}