chore: Bump to 4.11.0

This commit is contained in:
jstoobysmith 2024-09-04 06:28:46 -04:00
parent b6162217b7
commit 17f09022db
48 changed files with 404 additions and 137 deletions

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@ -85,6 +85,7 @@ variable {𝓵 : }
variable (μ2 : )
variable (h𝓵 : 0 < 𝓵)
include h𝓵
/-- The second term of the potential is non-negative. -/
lemma snd_term_nonneg (φ : HiggsField) (x : SpaceTime) :
0 ≤ 𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x := by
@ -93,11 +94,13 @@ lemma snd_term_nonneg (φ : HiggsField) (x : SpaceTime) :
simp_all only [normSq, gt_iff_lt, mul_nonneg_iff_of_pos_left, ge_iff_le, norm_nonneg, pow_nonneg,
and_self]
omit h𝓵
lemma as_quad (μ2 𝓵 : ) (φ : HiggsField) (x : SpaceTime) :
𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x + (- μ2) * ‖φ‖_H ^ 2 x + (- potential μ2 𝓵 φ x) = 0 := by
simp only [normSq, neg_mul, potential, neg_add_rev, neg_neg]
ring
include h𝓵
/-- The discriminant of the quadratic formed by the potential is non-negative. -/
lemma discrim_nonneg (φ : HiggsField) (x : SpaceTime) :
0 ≤ discrim 𝓵 (- μ2) (- potential μ2 𝓵 φ x) := by
@ -141,7 +144,7 @@ lemma bounded_below (φ : HiggsField) (x : SpaceTime) :
ring_nf at h1
rw [← neg_le_iff_add_nonneg'] at h1
rw [show 𝓵 * potential μ2 𝓵 φ x * 4 = (4 * 𝓵) * potential μ2 𝓵 φ x by ring] at h1
have h2 := (div_le_iff' (by simp [h𝓵] : 0 < 4 * 𝓵)).mpr h1
have h2 := (div_le_iff' (by simp [h𝓵] : 0 < 4 * 𝓵)).mpr h1
ring_nf at h2 ⊢
exact h2
@ -164,12 +167,14 @@ variable (h𝓵 : 0 < 𝓵)
-/
include h𝓵
lemma discrim_eq_zero_of_eq_bound (φ : HiggsField) (x : SpaceTime)
(hV : potential μ2 𝓵 φ x = - μ2 ^ 2 / (4 * 𝓵)) :
discrim 𝓵 (- μ2) (- potential μ2 𝓵 φ x) = 0 := by
rw [discrim, hV]
field_simp
include h𝓵
lemma normSq_of_eq_bound (φ : HiggsField) (x : SpaceTime)
(hV : potential μ2 𝓵 φ x = - μ2 ^ 2 / (4 * 𝓵)) :
‖φ‖_H ^ 2 x = μ2 / (2 * 𝓵) := by