I finally got my voting code, which I did not receive with the acceptance. I will try to reread your paper in the near future.
I indicated to Giovanni Amelino-Camelia the κ-Minkowski and his boost operator should have some connection to twistor theory. The boost operator P_μ that acts on [x_i, x_0] = ilx_i such that
P_μ > [x_i, x_0] = il P_μ > x_i
The coordinates (x_j, x_0) we write in spinor form
x_j = σ_j^{aa'}ω_{aa'}
x_0 = σ_0^{aa'}ω_{aa'},
where ω_{aa'} = ξ_a ω_{a'} ξ_{a'}ω_a. This commutator has the form
[x_i, x_0] = σ_j^{aa'}σ_0^{bb'}[ω_{aa'}, ω_{bb'}]
= iC^{cc'}_{aa'bb'} σ_j^{aa'} σ_0^{bb'} ω_{aa'}
= i|C| σ_j^{aa'}ω_{aa'}
where the magnitude of the structure matrix is |C| = l. In general this may be written for
x_j = σ_j^{aa'}ω_{aa'}
x_0 = σ_0^{aa'}ω_{aa'} iq_{aa'}π^{aa'},
where the commutator [ω_{aa'}, π^{bb'}] = iδ_a^bδ_{a'}^{b'} and the general form of the commutator is then
[x_i, x_0] = i|C| σ_j^{aa'}ω_{aa'} iσ_j^{aa'}q_{bb'}[ω_{aa'}, π^{bb''}
[x_i, x_0] = ilσ_j^{aa'}ω_{aa'} - σ_j^{aa'}q_{aa'}.
The boost operation B = 1 a^l_jP^j on the commutator [x_i, x_0] is then equivalent to the commutation between spinors [ω_a, ω'_b] for ω'_b = ω_b iq_{bb'}π^{b'},
[ω_a, ω'_b] = [ω_a, ω_b] iq_{bb'}[ω_a , π^{b'}]
= C^c_{ab} ω_c iq_{ab}.
Ed Witten demonstrated a "twistor revolution" in string theory. If this connection exists and can be explored further, it might mean that loop variables and other discrete quantum gravity ideas might bridge with string theory. It could then be that the two approaches will fix the various difficulties they have.
Cheers LC
Cheers
