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/-
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Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.Lorentz.RealVector.Basic
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import HepLean.PerturbationTheory.FieldStatistics.ExchangeSign
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import HepLean.SpaceTime.Basic
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import HepLean.PerturbationTheory.FieldStatistics.OfFinset
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/-!
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# Field structures
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-/
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/-- A field structure is a type of fields plus a specification of the
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statistics (fermionic or bosonic) of each field. -/
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structure FieldStruct where
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/-- The type of fields. This also includes anti-states. -/
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Fields : Type
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/-- The specification if a field is bosonic or fermionic. -/
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statistics : 𝓕 → FieldStatistic
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namespace FieldStruct
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variable (𝓕 : FieldStruct)
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/-- Negative asymptotic states are specified by a field and a momentum. -/
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def AsymptoticNegTime : Type := 𝓕.Fields × Lorentz.Contr 4
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/-- Positive asymptotic states are specified by a field and a momentum. -/
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def AsymptoticPosTime : Type := 𝓕.Fields × Lorentz.Contr 4
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/-- States specified by a field and a space-time position. -/
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def PositionStates : Type := 𝓕.Fields × SpaceTime
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2025-01-13 23:59:30 +01:00
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/-- The combination of asymptotic states and position states. -/
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inductive States (𝓕 : FieldStruct) where
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| negAsymp : 𝓕.AsymptoticNegTime → 𝓕.States
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| position : 𝓕.PositionStates → 𝓕.States
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| posAsymp : 𝓕.AsymptoticPosTime → 𝓕.States
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/-- Taking a state to its underlying field. -/
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def statesToField : 𝓕.States → 𝓕.Fields
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| States.negAsymp φ => φ.1
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| States.position φ => φ.1
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| States.posAsymp φ => φ.1
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/-- The statistics associated to a state. -/
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def statesStatistic : 𝓕.States → FieldStatistic := 𝓕.statistics ∘ 𝓕.statesToField
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/-- The field statistics associated with a state. -/
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scoped[FieldStruct] notation 𝓕 "|>ₛ" φ => statesStatistic 𝓕 φ
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/-- The field statistics associated with a list states. -/
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scoped[FieldStruct] notation 𝓕 "|>ₛ" φ => FieldStatistic.ofList
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(statesStatistic 𝓕) φ
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/-- The field statistic associated with a finite set-/
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scoped[FieldStruct] notation 𝓕 "|>ₛ" "⟨" f ","a "⟩"=> FieldStatistic.ofFinset
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(statesStatistic 𝓕) f a
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end FieldStruct
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