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auto-task(EffectivePotential): TODO to make Higgs potential polynomial basis-independent #1321

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auto-task(EffectivePotential): TODO to make Higgs potential polynomial basis-independent #1321

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auto-task(TwoHiggsDoublet): add TODO to define the Module instance
jstoobysmith Jun 29, 2026
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auto-task(EffectivePotential): TODO to make Higgs potential polynomia…
jstoobysmith Jun 29, 2026
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4 changes: 4 additions & 0 deletions Physlib/Particles/BeyondTheStandardModel/TwoHDM/Basic.lean
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Expand Up @@ -52,6 +52,10 @@ lemma ext_of_fst_snd {H1 H2 : TwoHiggsDoublet}
cases H1
cases H2
congr

TODO "Define the `Module ℂ TwoHiggsDoublet` instance (with its underlying `AddCommGroup`),
making the configuration space `TwoHiggsDoublet` a complex vector space via the componentwise
structure on the two `HiggsVec` doublets `Φ1` and `Φ2`."
/-!
## B. Gauge group actions
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5 changes: 5 additions & 0 deletions Physlib/Particles/StandardModel/HiggsBoson/EffectivePotential.lean
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Expand Up @@ -95,6 +95,11 @@ lemma polynomial_totalDegree {V : EffectivePotential} {n : ℕ} (h : HasMaxMassD
lemma apply_eq_polynomial {V : EffectivePotential} {n : ℕ} (h : HasMaxMassDimLE V n)
(φ : HiggsVec) : V φ = (polynomial V h).eval φ.toRealScalars := (Classical.choose_spec h).1 φ

TODO "Reformulate `HasMaxMassDimLE` (and `polynomial`) to use the basis-independent polynomial
ring `MvPolynomial (Module.Dual ℝ HiggsVec) ℝ` rather than `MvPolynomial (Fin 4) ℝ`, so that the
effective potential is expressed without reference to the explicit coordinate map
`HiggsVec.toRealScalars`."

/-!
## C. Terms of a given mass dimension
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