diff --git a/PhysLean/CondensedMatter/TightBindingChain/Basic.lean b/PhysLean/CondensedMatter/TightBindingChain/Basic.lean index 61f03e9a6..dc37fcf0f 100644 --- a/PhysLean/CondensedMatter/TightBindingChain/Basic.lean +++ b/PhysLean/CondensedMatter/TightBindingChain/Basic.lean @@ -538,7 +538,7 @@ lemma energyEigenstate_orthogonal : simp only [Nat.cast_one] at h2 h1 calc _ = Complex.exp (Complex.I * k2 * 1 * T.N * T.a - Complex.I * k1 * 1 * T.N * T.a) := by ring_nf - _ = 1 := by rw [Complex.exp_sub, h2, h1, div_one] + _ = 1 := by rw [Complex.exp_sub, h2, h1, div_one] have hω_ne_one : ω ≠ 1 := by intro hω_eq_one apply hne diff --git a/PhysLean/Particles/BeyondTheStandardModel/TwoHDM/Potential.lean b/PhysLean/Particles/BeyondTheStandardModel/TwoHDM/Potential.lean index 61abb57e5..7f2660fc0 100644 --- a/PhysLean/Particles/BeyondTheStandardModel/TwoHDM/Potential.lean +++ b/PhysLean/Particles/BeyondTheStandardModel/TwoHDM/Potential.lean @@ -432,6 +432,17 @@ lemma potentialIsBounded_iff_exists_forall_reduced (P : PotentialParameters) : · nlinarith · grind +lemma massTermReduced_pos_of_quarticTermReduced_zero_potentialIsBounded (P : PotentialParameters) + (hP : PotentialIsBounded P) (k : EuclideanSpace ℝ (Fin 3)) + (hk : ‖k‖ ^ 2 ≤ 1) (hq : quarticTermReduced P k = 0) : 0 ≤ massTermReduced P k := by + rw [potentialIsBounded_iff_exists_forall_reduced] at hP + obtain ⟨c, hc₀, hc⟩ := hP + specialize hc k hk + rw [hq] at hc + simp only [le_refl, mul_zero, zero_mul, sq_nonpos_iff, true_and] at hc + generalize massTermReduced P k = j2 at * + grind + @[sorryful] lemma potentialIsBounded_iff_forall_reduced (P : PotentialParameters) : PotentialIsBounded P ↔ ∀ k : EuclideanSpace ℝ (Fin 3), ‖k‖ ^ 2 ≤ 1 → diff --git a/PhysLean/Relativity/Tensors/RealTensor/ToComplex.lean b/PhysLean/Relativity/Tensors/RealTensor/ToComplex.lean index 1e88218cb..2e3760f9d 100644 --- a/PhysLean/Relativity/Tensors/RealTensor/ToComplex.lean +++ b/PhysLean/Relativity/Tensors/RealTensor/ToComplex.lean @@ -227,8 +227,7 @@ noncomputable def evalTColorToComplex {n : ℕ} permT (S := complexLorentzTensor) (σ := (id : Fin n → Fin n)) (by -- transport ((colorToComplex ∘ c) ∘ i.succAbove) and (colorToComplex ∘ (c ∘ i.succAbove)) - simp [Function.comp_apply] - ) + simp [Function.comp_apply]) ((TensorSpecies.Tensor.evalT (S := complexLorentzTensor) (c := (colorToComplex ∘ c)) i (evalIdxToComplex (c := c) i b)) t)