PhysLean/HepLean/StandardModel/Basic.lean

/-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license.
Authors: Joseph Tooby-Smith
-/
import Mathlib.Data.Complex.Exponential
import Mathlib.Geometry.Manifold.Instances.Real
import Mathlib.LinearAlgebra.Matrix.ToLin
/-!
# The Standard Model

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)

-/
universe v u
namespace StandardModel

open Manifold
open Matrix
open Complex
open ComplexConjugate

/-- The global gauge group of the standard model. TODO: Generalize to quotient. -/
abbrev GaugeGroup : Type :=
  specialUnitaryGroup (Fin 3) ℂ × specialUnitaryGroup (Fin 2) ℂ × unitary ℂ

end StandardModel