feat: Add 2HDM potential

HepLean.lean

@@ -47,6 +47,7 @@ import HepLean.AnomalyCancellation.SMNu.PlusU1.HyperCharge
 import HepLean.AnomalyCancellation.SMNu.PlusU1.PlaneNonSols
 import HepLean.AnomalyCancellation.SMNu.PlusU1.QuadSol
 import HepLean.AnomalyCancellation.SMNu.PlusU1.QuadSolToSol
+import HepLean.BeyondTheStandardModel.TwoHDM.Basic
 import HepLean.FlavorPhysics.CKMMatrix.Basic
 import HepLean.FlavorPhysics.CKMMatrix.Invariants
 import HepLean.FlavorPhysics.CKMMatrix.PhaseFreedom

HepLean/BeyondTheStandardModel/TwoHDM/Basic.lean

@@ -0,0 +1,29 @@
+/-
+Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
+Released under Apache 2.0 license.
+Authors: Joseph Tooby-Smith
+-/
+import HepLean.StandardModel.HiggsBoson.Basic
+
+namespace TwoHDM
+
+open StandardModel
+open ComplexConjugate
+
+noncomputable section
+
+/-- The potential of the two Higgs doublet model.  -/
+def potential (Φ1 Φ2 : higgsField)
+    (m11Sq m22Sq lam₁ lam₂ lam₃ lam₄ : ℝ) (m12Sq lam₅ lam₆ lam₇ : ℂ) (x : spaceTime) : ℝ :=
+  m11Sq * Φ1.normSq x  + m22Sq * Φ2.normSq x
+  - (m12Sq * (Φ1.innerProd Φ2) x + conj m12Sq * (Φ2.innerProd Φ1) x).re
+  + 1/2 * lam₁ * Φ1.normSq x ^ 2 + 1/2 * lam₂ * Φ2.normSq x ^ 2
+  + lam₃ * Φ1.normSq x * Φ2.normSq x
+  + lam₄ * ‖Φ1.innerProd Φ2 x‖
+  + (1/2 * lam₅ * (Φ1.innerProd Φ2) x ^ 2 + 1/2 * conj lam₅ * (Φ2.innerProd Φ1) x ^ 2).re
+  + (lam₆ * Φ1.normSq x * (Φ1.innerProd Φ2) x + conj lam₆ * Φ1.normSq x * (Φ2.innerProd Φ1) x).re
+  + (lam₇ * Φ2.normSq x * (Φ1.innerProd Φ2) x + conj lam₇ * Φ2.normSq x * (Φ2.innerProd Φ1) x).re
+
+
+end
+end TwoHDM

HepLean/StandardModel/HiggsBoson/Basic.lean

@@ -100,6 +100,10 @@ lemma apply_im_smooth (φ : higgsField) (i : Fin 2):
     Smooth 𝓘(ℝ, spaceTime) 𝓘(ℝ, ℝ) (imCLM ∘ (fun (x : spaceTime) =>  (φ x i))) :=
   Smooth.comp (ContinuousLinearMap.smooth imCLM) (φ.apply_smooth i)
 
+/-- Given two `higgsField`, the map `spaceTime → ℂ` obtained by taking their inner product. -/
+def innerProd (φ1 φ2 : higgsField) : spaceTime → ℂ := fun x => ⟪φ1 x, φ2 x⟫_ℂ
+
+
 /-- Given a `higgsField`, the map `spaceTime → ℝ` obtained by taking the square norm of the
  higgs vector.  -/
 @[simp]