Time Space Basis add Haar
SpaceTime.timeSpaceBasis_addHaar
Project documentation
The equivalence on of SpaceTime taking (1, 0, 0, ...) to of (c, 0, 0, ....) and keeping all other components the same. -/ def timeSpaceBasisEquiv {d : ℕ} (c : SpeedOfLight) : SpaceTime d ≃L[ℝ] SpaceTime d where toFun x := fun μ => match μ with | Sum.inl 0 => c.val * x (Sum.inl 0) | Sum.inr i => x (Sum.inr i) invFun x := fun μ => match μ with | Sum.i...
Exact Lean statement
lemma timeSpaceBasis_addHaar {d : ℕ} (c : SpeedOfLight := 1) :
(timeSpaceBasis (d := d) c).addHaar = (ENNReal.ofReal (c⁻¹)) • volumeFormal artifact
Lean source
lemma timeSpaceBasis_addHaar {d : ℕ} (c : SpeedOfLight := 1) : (timeSpaceBasis (d := d) c).addHaar = (ENNReal.ofReal (c⁻¹)) • volume := by rw [timeSpaceBasis_eq_map_basis c, ← Module.Basis.map_addHaar] have h1 := MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar (f := (timeSpaceBasisEquiv (d := d) c).toLinearMap) (μ := Lorentz.Vector.basis.addHaar) (by simp [← LinearEquiv.coe_det, det_timeSpaceBasisEquiv]) simp at h1 rw [h1] simp [← LinearEquiv.coe_det, det_timeSpaceBasisEquiv] congr simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/SpaceAndTime/SpaceTime/Basic.lean:527-537
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