κ-deformed oscillators: Deformed multiplication versus deformed flip operator and multiparticle clusters

We transform the oscillator algebra with κ-deformed multiplication rule, proposed in [1, 2], into the oscillator algebra with κ-deformed flip operator and standard multiplication. We recall that the κ-multiplication of the κ-oscillators puts them off-shell. We study the explicit forms of modified mass-shell conditions in both formulations: with κ-multiplication and with κ-flip operation. On the example of κ-deformed 2-particle states we study the clustered nonfactorizable form of the κ-deformed multiparticle states. We argue that the κ-deformed star product of two free fields leads in similar way to a nonfactorizable κ-deformed bilocal field. We conclude with general remarks concerning the κ-deformed n-particle clusters and κ-deformed star product of n fields.