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In order to obtain free kappa-deformed quantum fields (with c-number commutators) we proposed new concept of kappa-deformed oscillator algebra [1] and the modification of kappa-star product [2], implementing in the product of two quantum fields the change of standard kappa-deformed mass-shell conditions. We recall here that the kappa-deformed oscillators recently introduced in [3]-[5] lie on standard kappa-deformed mass-shell. Firstly, we study kappa-deformed fields with the standard kappa-star product, what implies that in the oscillator algebra the corresponding kappa-deformed oscillators lie on standard kappa-deformed mass-shell. We argue that for the kappa-deformed algebra of such field oscillators which carry fourmomenta on kappa-deformed mass-shell it is not possible to obtain the free quantum kappa-deformed fields with the c-number commutators. Further, we study kappa-deformed quantum fields with the modified kappa-star product which implies the modification of kappa-deformed mass-shell. We obtain large class of kappa-deformed statistics depending on six arbitrary functions which provides the c-number field commutator functions. Such general class of kappa-oscillators can be described as the kappa-deformation of standard oscillator algebra obtained by composing general kappa-deformed multiplication with the deformation of the flip operator.
We describe the deformed E.T. quantization rules for kappa-deformed free quantum fields, and relate these rules with the kappa-deformed algebra of field oscillators.
We present a construction of $kappa$-deformed complex scalar field theory with the objective of shedding light on the way discrete symmetries and CPT invariance are affected by the deformation. Our starting point is the observation that, in order to
We present the quantum $kappa$-deformation of BMS symmetry, by generalizing the lightlike $kappa$-Poincare Hopf algebra. On the technical level, our analysis relies on the fact that the lightlike $kappa$-deformation of Poincare algebra is given by a
We transform the oscillator algebra with kappa-deformed multiplication rule, proposed in [1],[2], into the oscillator algebra with kappa-deformed flip operator and standard multiplication. We recall that the kappa-multiplication of the kappa-oscillat
The classical $r$-matrix for $N=1$ superPoincar{e} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{e} supergroup. The standard correspondence principle between the even (odd) Pois