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refactor: Lint

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jstoobysmith 2024-07-11 09:55:23 -04:00
parent 92cca4c6df
commit e40172ce5a
4 changed files with 43 additions and 18 deletions
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1
HepLean/SpaceTime/LorentzGroup/Basic.lean
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@ -16,7 +16,6 @@ We define the Lorentz group.
-/
/-! TODO: Show that the Lorentz is a Lie group. -/
/-! TODO: Prove restricted Lorentz group equivalent to connected component of identity. -/
noncomputable section

10
HepLean/SpaceTime/LorentzGroup/Proper.lean
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@ -7,7 +7,9 @@ import HepLean.SpaceTime.LorentzGroup.Basic
/-!
# The Proper Lorentz Group
We define the give a series of lemmas related to the determinant of the lorentz group.
The proper Lorentz group is the subgroup of the Lorentz group with determinant `1`.
We define the give a series of lemmas related to the determinant of the Lorentz group.
-/
@ -23,7 +25,7 @@ open minkowskiMetric
variable {d : ℕ}
/-- The determinant of a member of the lorentz group is `1` or `-1`. -/
/-- The determinant of a member of the Lorentz group is `1` or `-1`. -/
lemma det_eq_one_or_neg_one (Λ : 𝓛 d) : Λ.1.det = 1 ∨ Λ.1.det = -1 := by
have h1 := (congrArg det ((mem_iff_self_mul_dual).mp Λ.2))
simp [det_mul, det_dual] at h1
@ -47,7 +49,7 @@ def coeForℤ₂ : C(({-1, 1} : Set ℝ), ℤ₂) where
haveI : DiscreteTopology ({-1, 1} : Set ℝ) := discrete_of_t1_of_finite
exact continuous_of_discreteTopology
/-- The continuous map taking a lorentz matrix to its determinant. -/
/-- The continuous map taking a Lorentz matrix to its determinant. -/
def detContinuous : C(𝓛 d, ℤ₂) :=
ContinuousMap.comp coeForℤ₂ {
toFun := fun Λ => ⟨Λ.1.det, Or.symm (LorentzGroup.det_eq_one_or_neg_one _)⟩,
@ -73,7 +75,7 @@ lemma detContinuous_eq_iff_det_eq (Λ Λ' : LorentzGroup d) :
· intro h
simp [detContinuous, h]
/-- The representation taking a lorentz matrix to its determinant. -/
/-- The representation taking a Lorentz matrix to its determinant. -/
@[simps!]
def detRep : 𝓛 d →* ℤ₂ where
toFun Λ := detContinuous Λ

14
HepLean/SpaceTime/LorentzGroup/Restricted.lean Normal file
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@ -0,0 +1,14 @@
/-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license.
Authors: Joseph Tooby-Smith
-/
/-!
# The Restricted Lorentz Group
This file is currently a stub.
-/
/-! TODO: Add definition of the restricted Lorentz group. -/
/-! TODO: Prove member of the restricted Lorentz group is combo of boost and rotation. -/
/-! TODO: Prove restricted Lorentz group equivalent to connected component of identity. -/