Joseph Tooby-Smith
GitHub
commit
8229c1a752
10 changed files with 14 additions and 37 deletions
|
|
@ -13,12 +13,10 @@ This file defines the basic structures for the anomaly cancellation conditions.
|
|||
|
||||
It defines a module structure on the charges, and the solutions to the linear ACCs.
|
||||
|
||||
## TODO
|
||||
|
||||
- Derive ACC systems from gauge algebras and fermionic representations.
|
||||
- Relate ACCSystems to algebraic varieties.
|
||||
|
||||
-/
|
||||
/-! TODO: Derive an ACC system from a guage algebra and fermionic representations. -/
|
||||
/-! TODO: Relate ACC Systems to algebraic varieties. -/
|
||||
/-! TODO: Refactor whole file, and dependent files. -/
|
||||
|
||||
/-- A system of charges, specified by the number of charges. -/
|
||||
structure ACCSystemCharges where
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
||||
|
|
|
|||
|
|
@ -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. -/
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
||||
|
|
|
|||
|
|
@ -11,12 +11,8 @@ import Mathlib.LinearAlgebra.Matrix.ToLin
|
|||
|
||||
This file defines the basic properties of the standard model in particle physics.
|
||||
|
||||
## TODO
|
||||
|
||||
- Change the gauge group to a quotient of SU(3) x SU(2) x U(1) by a subgroup of ℤ₆.
|
||||
(see e.g. pg 97 of http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf)
|
||||
|
||||
-/
|
||||
/-! TODO: Redefine the gauge group as a quotient of SU(3) x SU(2) x U(1) by a subgroup of ℤ₆. -/
|
||||
universe v u
|
||||
namespace StandardModel
|
||||
|
||||
|
|
|
|||
|
|
@ -27,6 +27,8 @@ This file is a import of `SM.HiggsBoson.Basic`.
|
|||
- We use conventions given in: [Review of Particle Physics, PDG][ParticleDataGroup:2018ovx]
|
||||
|
||||
-/
|
||||
/-! TODO: Move potential to a seperate file, and combine with HiggsBoson.Basic. -/
|
||||
|
||||
universe v u
|
||||
namespace StandardModel
|
||||
noncomputable section
|
||||
|
|
|
|||
|
|
@ -17,8 +17,6 @@ This program finds all instances of `/<!> TODO: ...` (without the `<>`) in HepLe
|
|||
Parts of this file are adapted from `Mathlib.Tactic.Linter.TextBased`,
|
||||
authored by Michael Rothgang.
|
||||
|
||||
|
||||
-
|
||||
-/
|
||||
open Lean System Meta
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue