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

Update Boosts.lean

Browse source
This commit is contained in:
Pietro Monticone 2024-06-08 01:53:28 +02:00
parent e6bea53658
commit 2a84c3b87e
1 changed files with 6 additions and 6 deletions
Download patch file Download diff file Expand all files Collapse all files

12
HepLean/SpaceTime/LorentzGroup/Boosts.lean
View file

@ -12,14 +12,14 @@ import Mathlib.Topology.Constructions
This file defines those Lorentz which are boosts. This file defines those Lorentz which are boosts.
We first define generalised boosts, which are restricted lorentz transforamations taking We first define generalised boosts, which are restricted lorentz transformations taking
a four velocity `u` to a four velcoity `v`. a four velocity `u` to a four velocity `v`.
A boost is the speical case of a generalised boost when `u = stdBasis 0`. A boost is the special case of a generalised boost when `u = stdBasis 0`.
## TODO ## TODO
- Show that generalised boosts are in the restircted Lorentz group. - Show that generalised boosts are in the restricted Lorentz group.
- Define boosts. - Define boosts.
## References ## References
@ -35,7 +35,7 @@ namespace lorentzGroup
open FourVelocity open FourVelocity
/-- An auxillary linear map used in the definition of a genearlised boost. -/ /-- An auxillary linear map used in the definition of a generalised boost. -/
def genBoostAux₁ (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime where def genBoostAux₁ (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime where
toFun x := (2 * ηLin x u) • v.1.1 toFun x := (2 * ηLin x u) • v.1.1
map_add' x y := by map_add' x y := by
@ -61,7 +61,7 @@ def genBoostAux₂ (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime where
rw [mul_div_assoc, neg_mul_eq_mul_neg, smul_smul] rw [mul_div_assoc, neg_mul_eq_mul_neg, smul_smul]
rfl rfl
/-- An genearlised boost. This is a Lorentz transformation which takes the four velocity `u` /-- An generalised boost. This is a Lorentz transformation which takes the four velocity `u`
to `v`. -/ to `v`. -/
def genBoost (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime := def genBoost (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime :=
LinearMap.id + genBoostAux₁ u v + genBoostAux₂ u v LinearMap.id + genBoostAux₁ u v + genBoostAux₂ u v