`half`

definition

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module: IndisputableMonolith.QFT.SpinStatistics
domain: QFT
line: 67 · github
papers citing: none yet

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IndisputableMonolith.QFT.SpinStatistics on GitHub at line 67.

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formal source

  64def zero : Spin := ofInt 0
  65
  66/-- Spin 1/2 (electron, quarks). -/
  67def half : Spin := halfInt 1
  68
  69/-- Spin 1 (photon, W/Z, gluon). -/
  70def one : Spin := ofInt 1
  71
  72/-- Spin 3/2 (hypothetical gravitino). -/
  73def threeHalves : Spin := halfInt 3
  74
  75/-- Spin 2 (graviton). -/
  76def two : Spin := ofInt 2
  77
  78/-- The actual spin value as a real number. -/
  79noncomputable def value (s : Spin) : ℝ := s.twice / 2
  80
  81/-- Is this a half-integer spin (fermion)? -/
  82def isHalfInteger (s : Spin) : Prop := s.twice % 2 = 1
  83
  84/-- Is this an integer spin (boson)? -/
  85def isInteger (s : Spin) : Prop := s.twice % 2 = 0
  86
  87/-- Decidable instance for half-integer check. -/
  88instance : DecidablePred isHalfInteger := fun s =>
  89  if h : s.twice % 2 = 1 then isTrue h else isFalse h
  90
  91/-- Decidable instance for integer check. -/
  92instance : DecidablePred isInteger := fun s =>
  93  if h : s.twice % 2 = 0 then isTrue h else isFalse h
  94
  95/-- Spin is either integer or half-integer. -/
  96theorem int_or_half (s : Spin) : s.isInteger ∨ s.isHalfInteger := by
  97  unfold isInteger isHalfInteger

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