I'm trying to plot a 3D function on axes F(p,q), q^2, and p^2, with p and q being Four-vectors:
p^μ Subscript[p, μ] = p^0 Subscript[p, 0] - p^i Subscript[p, i]
q^μ Subscript[q, μ] = q^0 Subscript[q, 0] - q^i Subscript[q, i]
p^μ Subscript[q, μ] = (Subscript[p, 0] - Subscript[p, i])(Subscript[q, 0]- ubscript[q, i])
I need Wolfram to undestand this and produce the scalars, p^2, q^2, from p and q. This function has already been computed using the moment spaces and it is given by:
F[p_, q_] := PolyLog[2, (Subscript[λ, 1]
- Subscript[λ, 1] Sqrt[(1 - β)/(1 - α)])/(1 - Subscript[λ, 1] Sqrt[(1 - β)/(1 - α)])]
Where:
Subscript[λ, 1] = Sqrt[((ScalarProduct[p, q])^2
-p^2 q^2)]/Subscript[λ, 2]-1/Subscript[λ, 2]Sqrt[(ScalarProduct[p, q])^2
-p^2 q^2 - ((2 ScalarProduct[p, q] β - p^2)/(α - β)) ((p^2
- 2 α (ScalarProduct[p, q]))/(α - β))]
Subscript[λ, 2] = (2 ScalarProduct[p, q] β - p^2)/(α - β)
α = p^2/(2 ((ScalarProduct[p, q])^2 - p^2 q^2)) {-(q^2 - ScalarProduct[p, q])
+ Sqrt[q^2 (p - q)^2 + 4 ((ScalarProduct[p, q])^2 - p^2 q^2) 1^2/p^2]}
β = p^2/(2 ((ScalarProduct[p, q])^2 - p^2 q^2)) {-(q^2 - ScalarProduct[p, q])
- Sqrt[ q^2 (p - q)^2 + 4 ((ScalarProduct[p, q])^2 - p^2 q^2) 1^2/p^2]}
The graph must be a function that can be analyzed, including the imaginary part. When I tried to plot, there appeared a function rife with peaks, what I believe to be because Wolfram do not understand the dot product of p with q. That is, it is probably varying numbers for p and q and getting a result without taking into account that these quantities are Four-vectors. Thank you in advance.