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Use notes' sign convention for light cone basis

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This commit is contained in:
Aaron Fenyes 2024-07-17 23:07:34 -07:00
parent 01f44324c1
commit 69a704d414
5 changed files with 11 additions and 11 deletions
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10
engine-proto/gram-test/Engine.jl
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@ -39,7 +39,7 @@ rand_on_shell(shells::Array{<:Number}) = rand_on_shell(Random.default_rng(), she
# === elements ===
point(pos) = [pos; -1; 0.25 * dot(pos, pos)]
point(pos) = [pos; 1; 0.25 * dot(pos, pos)]
plane(normal, offset) = [normal; 0; offset]
@ -47,7 +47,7 @@ function sphere(center, radius)
dist_sq = dot(center, center)
[
center / radius;
-0.5 / radius;
0.5 / radius;
0.5 * (dist_sq / radius - radius)
]
end
@ -55,12 +55,12 @@ end
# === Gram matrix realization ===
# basis changes
nullmix = [Matrix{Int64}(I, 3, 3) zeros(Int64, 3, 2); zeros(Int64, 2, 3) [1 -1; 1 1]//2]
unmix = [Matrix{Int64}(I, 3, 3) zeros(Int64, 3, 2); zeros(Int64, 2, 3) [1 1; -1 1]]
nullmix = [Matrix{Int64}(I, 3, 3) zeros(Int64, 3, 2); zeros(Int64, 2, 3) [-1 1; 1 1]//2]
unmix = [Matrix{Int64}(I, 3, 3) zeros(Int64, 3, 2); zeros(Int64, 2, 3) [-1 1; 1 1]]
# the Lorentz form
## [old] Q = diagm([1, 1, 1, 1, -1])
Q = [Matrix{Int64}(I, 3, 3) zeros(Int64, 3, 2); zeros(Int64, 2, 3) [0 2; 2 0]]
Q = [Matrix{Int64}(I, 3, 3) zeros(Int64, 3, 2); zeros(Int64, 2, 3) [0 -2; -2 0]]
# project a matrix onto the subspace of matrices whose entries vanish at the
# given indices