feat: Basic field strength equalities#1068
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zhikaip
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I think the docstring should be fixed, whether the mathematical properties can be generalised can be left for future work
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| /-- The statement that `F = F^{μν} eᵤ ⊗ eᵥ` written explicitly, with | ||
| the components extracted via `toField`. -/ | ||
| lemma toFieldStrength_eq_sum_basis_eval {d} {A : ElectromagneticPotential d} : |
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does this work for a general SpaceTime d → Lorentz.Vector d ⊗[ℝ] Lorentz.Vector d type?
To me it seems a bit uneconomic to have these results proven specifically for one physical object only where presumably it's just mathematical manipulations, but maybe there are difficulties I'm not aware of
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maybe this is a more general discussion and out of scope for this particular PR, if that's the case I'm happy to approve it first
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I added a TODO item about this. I tried to do this but it needs a bit more API I think.
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| We define the field strength tensor `F_μν` in terms of the derivative of the |
do you mind fixing the indices throughout?
zhikaip
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thanks for the changes, approved.
I've been thinking whether FieldStrength should get its own type, but maybe that's a much larger design decision to be made. Either way I think separating the maths from the physics as much as possible (generalising the former, then applying) is probably the way to go throughout physlib
Adding some lemmas which rewrite the field strength in a more familiar form. These will eventually be used to remove all the
Tensorstuff from EM.