33 lines
1.2 KiB
Text
33 lines
1.2 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 HepLean.SpaceTime.LorentzTensor.Basic
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/-!
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# Notation for Lorentz Tensors
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This file is currently a stub.
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We plan to set up index-notation for dealing with tensors.
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Some examples:
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- `ψᵘ¹ᵘ²φᵤ₁` should correspond to the contraction of the first index of `ψ` and the
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only index of `φ`.
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- `ψᵘ¹ᵘ² = ψᵘ²ᵘ¹` should define the symmetry of `ψ` under the exchange of its indices.
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- `θᵤ₂(ψᵘ¹ᵘ²φᵤ₁) = (θᵤ₂ψᵘ¹ᵘ²)φᵤ₁` should correspond to an associativity properity of
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contraction.
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It should also be possible to define this generically for any `LorentzTensorStructure`.
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Further we plan to make easy to define tensors with indices. E.g. `(ψ : Tenᵘ¹ᵘ²ᵤ₃)`
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should correspond to a (real Lorentz) tensors with 3 indices, two upper and one lower.
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For `(ψ : Tenᵘ¹ᵘ²ᵤ₃)`, if one writes e.g. `ψᵤ₁ᵘ²ᵤ₃`, this should correspond to a
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lowering of the first index of `ψ`.
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Further, it will be nice if we can have implicit contractions of indices
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e.g. in Weyl fermions.
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-/
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