DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

refactor: Spellings

Browse source
This commit is contained in:
jstoobysmith 2025-02-08 13:07:54 +00:00
parent 4cd71f5ec6
commit 4a55351b72
33 changed files with 88 additions and 88 deletions
Download patch file Download diff file Expand all files Collapse all files

8
HepLean/Lorentz/MinkowskiMatrix.lean
View file

@ -29,7 +29,7 @@ variable {d : ℕ}
/-- Notation for `minkowskiMatrix`. -/
scoped[minkowskiMatrix] notation "η" => minkowskiMatrix
/-- The Minkowski matrix is self-inveting. -/
/-- The Minkowski matrix is self-inverting. -/
@[simp]
lemma sq : @minkowskiMatrix d * minkowskiMatrix = 1 := by
simp only [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, diagonal_mul_diagonal]
@ -55,8 +55,8 @@ lemma sq : @minkowskiMatrix d * minkowskiMatrix = 1 := by
lemma eq_transpose : minkowskiMatrixᵀ = @minkowskiMatrix d := by
simp only [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, diagonal_transpose]
/-- The deteminant of the Minkowski matrix is equal to `-1` to the power
of the number of spactial dimensions. -/
/-- The determinant of the Minkowski matrix is equal to `-1` to the power
of the number of spatial dimensions. -/
@[simp]
lemma det_eq_neg_one_pow_d : (@minkowskiMatrix d).det = (- 1) ^ d := by
simp [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal]
@ -68,7 +68,7 @@ lemma η_apply_mul_η_apply_diag (μ : Fin 1 ⊕ Fin d) : η μ μ * η μ μ =
| Sum.inl _ => simp [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal]
| Sum.inr _ => simp [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal]
/-- The Minkowski matix as a block matrix. -/
/-- The Minkowski matrix as a block matrix. -/
lemma as_block : @minkowskiMatrix d =
Matrix.fromBlocks (1 : Matrix (Fin 1) (Fin 1) ℝ) 0 0 (-1 : Matrix (Fin d) (Fin d) ℝ) := by
rw [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, ← fromBlocks_diagonal]