56 lines
1.8 KiB
Text
56 lines
1.8 KiB
Text
/-
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Copyright (c) 2024 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 Mathlib.Logic.Function.Basic
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import HepLean.Meta.Informal
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/-!
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# Wick Species
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Note: There is very likely a much better name for what we here call a Wick Species.
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A Wick Species is a structure containing the basic information needed to write wick contractions
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for a theory, and calculate their corresponding Feynman diagrams.
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-/
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/-! TODO: There should be some sort of notion of a group action on a Wick Species. -/
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namespace Wick
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/-- The basic structure needed to write down Wick contractions for a theory and
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calculate the corresponding Feynman diagrams.
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WARNING: This definition is not yet complete.
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-/
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structure Species where
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/-- The color of Field operators which appear in a theory.
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One may wish to call these `half-edges`, however we restrict this terminology
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to Feynman diagrams. -/
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𝓯 : Type
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/-- The map taking a field operator to its dual operator. -/
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ξ : 𝓯 → 𝓯
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/-- The condition that `ξ` is an involution. -/
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ξ_involutive : Function.Involutive ξ
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/-- The color of interaction terms which appear in a theory.
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One may wish to call these `vertices`, however we restrict this terminology
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to Feynman diagrams. -/
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𝓘 : Type
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/-- The fields associated to each interaction term. -/
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𝓘Fields : 𝓘 → Σ n, Fin n → 𝓯
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namespace Species
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variable (S : Species)
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informal_definition 𝓕 where
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math :≈ "The orbits of the involution `ξ`.
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May have to define a multiplicative action of ℤ₂ on `𝓯`, and
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take the orbits of this."
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physics :≈ "The different types of fields present in a theory."
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deps :≈ [``Species]
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end Species
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end Wick
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