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refactor: pass at removing double spaces

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jstoobysmith 2024-07-12 10:36:39 -04:00
parent 1fe51b2e04
commit 1133b883f3
19 changed files with 121 additions and 121 deletions
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14
HepLean/StandardModel/HiggsBoson/Potential.lean
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@ -34,7 +34,7 @@ open SpaceTime
/-- The Higgs potential of the form `- μ² * |φ|² + 𝓵 * |φ|⁴`. -/
@[simp]
def potential (μ2 𝓵 : ℝ ) (φ : HiggsField) (x : SpaceTime) : ℝ :=
def potential (μ2 𝓵 : ℝ ) (φ : HiggsField) (x : SpaceTime) : ℝ :=
- μ2 * ‖φ‖_H ^ 2 x + 𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x
/-!
@ -94,7 +94,7 @@ lemma snd_term_nonneg (φ : HiggsField) (x : SpaceTime) :
and_self]
lemma as_quad (μ2 𝓵 : ℝ) (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
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
@ -121,7 +121,7 @@ lemma eq_zero_at (φ : HiggsField) (x : SpaceTime)
ring_nf
linear_combination h2
lemma eq_zero_at_of_μSq_nonpos {μ2 : ℝ} (hμ2 : μ2 ≤ 0)
lemma eq_zero_at_of_μSq_nonpos {μ2 : ℝ} (hμ2 : μ2 ≤ 0)
(φ : HiggsField) (x : SpaceTime) (hV : potential μ2 𝓵 φ x = 0) : φ x = 0 := by
cases' (eq_zero_at μ2 h𝓵 φ x hV) with h1 h1
exact h1
@ -141,7 +141,7 @@ 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
@ -165,13 +165,13 @@ variable (h𝓵 : 0 < 𝓵)
-/
lemma discrim_eq_zero_of_eq_bound (φ : HiggsField) (x : SpaceTime)
(hV : potential μ2 𝓵 φ x = - μ2 ^ 2 / (4 * 𝓵)) :
(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
lemma normSq_of_eq_bound (φ : HiggsField) (x : SpaceTime)
(hV : potential μ2 𝓵 φ x = - μ2 ^ 2 / (4 * 𝓵)) :
(hV : potential μ2 𝓵 φ x = - μ2 ^ 2 / (4 * 𝓵)) :
‖φ‖_H ^ 2 x = μ2 / (2 * 𝓵) := by
have h1 := as_quad μ2 𝓵 φ x
rw [quadratic_eq_zero_iff_of_discrim_eq_zero _
@ -180,7 +180,7 @@ lemma normSq_of_eq_bound (φ : HiggsField) (x : SpaceTime)
exact ne_of_gt h𝓵
lemma eq_bound_iff (φ : HiggsField) (x : SpaceTime) :
potential μ2 𝓵 φ x = - μ2 ^ 2 / (4 * 𝓵) ↔ ‖φ‖_H ^ 2 x = μ2 / (2 * 𝓵) :=
potential μ2 𝓵 φ x = - μ2 ^ 2 / (4 * 𝓵) ↔ ‖φ‖_H ^ 2 x = μ2 / (2 * 𝓵) :=
Iff.intro (normSq_of_eq_bound μ2 h𝓵 φ x)
(fun h ↦ by
rw [potential, h]