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def definition def or abbrev

spaceTranslationFlow

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formal statement (Lean)

  81def spaceTranslationFlow : OneParamGroup RealAction where
  82  flow dx γ := spaceShift dx γ

proof body

Definition body.

  83  flow_zero γ := by funext s; simp [spaceShift]
  84  flow_add s t γ := by funext u; simp [spaceShift]; ring
  85
  86/-- **Momentum conservation from space-translation invariance.**
  87
  88    If a J-action functional is space-translation invariant, then by
  89    `noether_core` it is itself conserved along the space-translation
  90    flow. The conserved quantity is interpreted as the total momentum. -/

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