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def definition def or abbrev

PhaseRotation

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formal statement (Lean)

 160noncomputable def PhaseRotation : OneParamGroup ℂ where
 161  flow θ z := Complex.exp (θ * Complex.I) * z

proof body

Definition body.

 162  flow_zero z := by simp [Complex.exp_zero]
 163  flow_add s t z := by
 164    rw [← mul_assoc, ← Complex.exp_add]
 165    congr 1
 166    push_cast
 167    ring
 168
 169/-- **THEOREM**: Any phase-rotation-invariant function is conserved.
 170    (U(1) symmetry ⟹ Electric charge conserved) -/

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