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

refactor: Rename deltas in ACC conditions

Browse source
This commit is contained in:
jstoobysmith 2024-11-28 12:50:34 +00:00
parent d26f010cb2
commit 6f83f5a623
8 changed files with 367 additions and 355 deletions
Download patch file Download diff file Expand all files Collapse all files

8
HepLean/Lorentz/PauliMatrices/SelfAdjoint.lean
View file

@ -342,7 +342,7 @@ lemma σSAL_decomp (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
ring
/-- The component of a self-adjoint matrix in the direction `σ0` under
the basis formed by the covaraiant Pauli matrices. -/
the basis formed by the covaraiant Pauli matrices. -/
@[simp]
lemma σSAL_repr_inl_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
σSAL.repr M (Sum.inl 0) = 1 / 2 * Matrix.trace (σ0 * M.1) := by
@ -359,7 +359,7 @@ lemma σSAL_repr_inl_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
simp [σSAL]
/-- The component of a self-adjoint matrix in the direction `-σ1` under
the basis formed by the covaraiant Pauli matrices. -/
the basis formed by the covaraiant Pauli matrices. -/
@[simp]
lemma σSAL_repr_inr_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
σSAL.repr M (Sum.inr 0) = - 1 / 2 * Matrix.trace (σ1 * M.1) := by
@ -376,7 +376,7 @@ lemma σSAL_repr_inr_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
simp [σSAL]
/-- The component of a self-adjoint matrix in the direction `-σ2` under
the basis formed by the covaraiant Pauli matrices. -/
the basis formed by the covaraiant Pauli matrices. -/
@[simp]
lemma σSAL_repr_inr_1 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
σSAL.repr M (Sum.inr 1) = - 1 / 2 * Matrix.trace (σ2 * M.1) := by
@ -393,7 +393,7 @@ lemma σSAL_repr_inr_1 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
simp [σSAL]
/-- The component of a self-adjoint matrix in the direction `-σ3` under
the basis formed by the covaraiant Pauli matrices. -/
the basis formed by the covaraiant Pauli matrices. -/
@[simp]
lemma σSAL_repr_inr_2 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
σSAL.repr M (Sum.inr 2) = - 1 / 2 * Matrix.trace (σ3 * M.1) := by