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jstoobysmith 2024-07-09 16:31:26 -04:00
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10 changed files with 14 additions and 37 deletions
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8
HepLean/SpaceTime/CliffordAlgebra.lean
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@ -9,13 +9,9 @@ import Mathlib.Analysis.Complex.Basic
This file defines the Gamma matrices.
## TODO
- Prove that the algebra generated by the gamma matrices is isomorphic to the
Clifford algebra associated with spacetime.
- Include relations for gamma matrices.
-/
/-! TODO: Prove algebra generated by gamma matrices is isomorphic to Clifford algebra. -/
/-! TODO: Define relations between the gamma matrices. -/
namespace spaceTime
open Complex

1
HepLean/SpaceTime/LorentzAlgebra/Basis.lean
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@ -15,3 +15,4 @@ This file is waiting for Lorentz Tensors to be done formally, before
it can be completed.
-/
/-! TODO: Define the standard basis of the Lorentz algebra. -/

9
HepLean/SpaceTime/LorentzGroup/Basic.lean
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@ -10,18 +10,13 @@ import HepLean.SpaceTime.LorentzVector.NormOne
We define the Lorentz group.
## TODO
- Show that the Lorentz is a Lie group.
- Prove that the restricted Lorentz group is equivalent to the connected component of the
identity.
- Define the continuous maps from `ℝ³` to `restrictedLorentzGroup` defining boosts.
## References
- http://home.ku.edu.tr/~amostafazadeh/phys517_518/phys517_2016f/Handouts/A_Jaffi_Lorentz_Group.pdf
-/
/-! TODO: Show that the Lorentz is a Lie group. -/
/-! TODO: Prove restricted Lorentz group equivalent to connected component of identity. -/
noncomputable section

5
HepLean/SpaceTime/LorentzGroup/Rotations.lean
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@ -11,11 +11,8 @@ import Mathlib.Topology.Constructions
This file describes the embedding of `SO(3)` into `LorentzGroup 3`.
## TODO
Generalize to arbitrary dimensions.
-/
/-! TODO: Generalize the inclusion of rotations into LorentzGroup to abitary dimension. -/
noncomputable section
namespace LorentzGroup

5
HepLean/SpaceTime/LorentzVector/AsSelfAdjointMatrix.lean
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@ -13,11 +13,8 @@ and the vector space of 2×2-complex self-adjoint matrices.
In this file we define this linear equivalence in `toSelfAdjointMatrix`.
## TODO
If possible generalize to arbitrary dimensions.
-/
/-! TODO: Generalize rep of Lorentz vector as a self-adjoint matrix to arbitary dimension. -/
namespace SpaceTime
open Matrix

5
HepLean/SpaceTime/SL2C/Basic.lean
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@ -124,12 +124,9 @@ def toLorentzGroup : SL(2, ℂ) →* LorentzGroup 3 where
The homomorphism `toLorentzGroup` restricts to a homomorphism to the restricted Lorentz group.
In this section we will define this homomorphism.
### TODO
Complete this section.
-/
/-! TODO: Define homomorphism from `SL(2, ℂ)` to the restricted Lorentz group. -/
end
end SL2C