Issue with 4D dot product?

[jpivarski]

Discussed in #147

^{Originally posted by wcosyn October 27, 2021}
I was using the package to do some relativistic kinematics calculations and noticed the following strange behavior. I would assume the 4D dot product to be the Lorentz inner product (so metric ---+), but it seems for some situations it reverts to a Cartesian inner product (metric ----). I would assume this is a bug as I wouldn't expect this sort of behavior or saw anything mentioned in the documentation that would explain it.

Here is an example that at least on my system shows the behavior. Simply flipping the sign of the fourvector SmuT yields the Cartesian instead of the Lorentz inner product. As a note, SmuT is constructed such that it is a spatial unit vector and (SmuT*P) should be zero.

import numpy as np
import vector

Ep = 275 #GeV
massp = 0.938 # GeV
theta_c = 25.*1.E-03
ppnorm = np.sqrt(Ep*Ep-massp*massp)

pp = vector.obj(pz=ppnorm*np.cos(theta_c),px=-ppnorm*np.sin(theta_c),py=0.,E=Ep)

pp_plus = pp.E+pp.pz

S_min = 2.*pp.px/(pp.E+pp.pz)
SmuT = vector.obj(E=0.5*(S_min),px=1.,py=0.,pz=0.5*(-S_min))

print("ST^2",SmuT.M2)
print("S dot P Lorentz", pp.dot(SmuT),-pp.dot(-SmuT))
print("Cartesian+: ",pp.E*SmuT.E+pp.px*SmuT.px+pp.py*SmuT.py+pp.pz*SmuT.pz)

Output:

ST^2 -1.0
S dot P Lorentz 6.875338094560275 -4.440892098500626e-16
Cartesian+: -6.875338094560275

I get similar behaviour in other situations, where changing some components of fourvectors flips a Lorentz inner product to a Cartesian one, seemingly at random.

[jpivarski]

@wcosyn It's not computing a Cartesian dot product—I followed the dispatch mechanism, and it always goes to vector._compute.lorentz.dot. The problem was that this dot product was deliberately defined as

rather than

I can't imagine what possessed me to put an absolute value around the product of the temporal components. PR #148 has a fix, and it's simply to remove the absolute value: 66e981b.

Thanks for catching it!