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feat(gamma-relations): Update matrix definition of gamma-matrices

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David Feng 2024-11-04 20:08:57 -05:00
parent db8732f2bf
commit b10d123a1f
1 changed files with 4 additions and 4 deletions
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8
HepLean/SpaceTime/CliffordAlgebra.lean
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@ -19,19 +19,19 @@ noncomputable section diracRepresentation
/-- The γ⁰ gamma matrix in the Dirac representation. -/
def γ0 : Matrix (Fin 4) (Fin 4) ℂ :=
![![1, 0, 0, 0], ![0, 1, 0, 0], ![0, 0, -1, 0], ![0, 0, 0, -1]]
!![1, 0, 0, 0; 0, 1, 0, 0; 0, 0, -1, 0; 0, 0, 0, -1]
/-- The γ¹ gamma matrix in the Dirac representation. -/
def γ1 : Matrix (Fin 4) (Fin 4) ℂ :=
![![0, 0, 0, 1], ![0, 0, 1, 0], ![0, -1, 0, 0], ![-1, 0, 0, 0]]
!![0, 0, 0, 1; 0, 0, 1, 0; 0, -1, 0, 0; -1, 0, 0, 0]
/-- The γ² gamma matrix in the Dirac representation. -/
def γ2 : Matrix (Fin 4) (Fin 4) ℂ :=
![![0, 0, 0, - I], ![0, 0, I, 0], ![0, I, 0, 0], ![-I, 0, 0, 0]]
!![0, 0, 0, - I; 0, 0, I, 0; 0, I, 0, 0; -I, 0, 0, 0]
/-- The γ³ gamma matrix in the Dirac representation. -/
def γ3 : Matrix (Fin 4) (Fin 4) ℂ :=
![![0, 0, 1, 0], ![0, 0, 0, -1], ![-1, 0, 0, 0], ![0, 1, 0, 0]]
!![0, 0, 1, 0; 0, 0, 0, -1; -1, 0, 0, 0; 0, 1, 0, 0]
/-- The γ⁵ gamma matrix in the Dirac representation. -/
def γ5 : Matrix (Fin 4) (Fin 4) ℂ := I • (γ0 * γ1 * γ2 * γ3)